# CO2 evasion along streams driven by groundwater inputs and geomorphic controls

Clément Duvert, David E. Butman, Anne Marx, Olivier Ribolzi, Lindsay B. Hutley

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Clément Duvert, David E. Butman, Anne Marx, Olivier Ribolzi, Lindsay B. Hutley. CO2 evasion along streams driven by groundwater inputs and geomorphic controls. Nature Geoscience, 2018, 11, pp.813-818. 10.1038/s41561-018-0245-y. insu-03661392

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# CO₂ evasion along streams driven by groundwater inputs and geomorphic controls

Clément Duvert<fnref n="1" />*, David E. Butman², Anne Marx³, Olivier Ribolzi⁴ and Lindsay B. Hutley<fnref n="1" />

Headwaters are hotspots of carbon dioxide (CO₂) evasion from rivers. While emerging evidence suggests that groundwater contributes disproportionately to CO₂ in headwater streams, the processes of CO₂ delivery to streams and subsequent evasion to the atmosphere remain largely unknown. Here we show the variability of CO₂ input and evasion fluxes based on coupled measurements of dissolved CO₂ along streams and in adjacent groundwater from two headwater catchments of the tropical and temperate zones. We find that the processes can be highly localized in both space and time. Spatially, they are significantly influenced by heterogeneities in the subsurface and stream landscape; temporally, they predominantly occur during the transient activation of connected subsurface water flows. We highlight sharp increases and decreases in the stream CO₂ flux, and suggest that current models fail to capture the true magnitude of CO₂ evasion. The high spatial and temporal variability of CO₂ input from groundwater and evasion to the atmosphere makes accurate assessment of CO₂ evasion fluxes difficult, and will require a collaborative effort by catchment hydrologists and aquatic ecologists to fully understand the contribution of groundwater to stream CO₂ emissions.

Rivers receive large inputs of terrestrial carbon (C), which they actively process, store and release<fnref n="1" />. There is now consensus that a considerable part of the C transported by rivers is returned to the atmosphere via evasion of CO₂ (refs ²⁻⁵). However, major unknowns remain as to the magnitude and rate of the global riverine CO₂ evasion flux⁶,⁷, which raises concerns about potential overestimations of the terrestrial C sink⁸. Growing interest in better constraining the riverine CO₂ evasion flux has resulted in a four-fold increase of global estimates over the last decade, from 0.8 Pg C y⁻<fnref n="1" /> (ref. <fnref n="1" />) to 2.9 Pg C y⁻<fnref n="1" /> for the latest available estimate⁹. This value is of similar magnitude to the global terrestrial C sink of 3.1 Pg C y⁻<fnref n="1" /> (ref. ¹⁰) but is not, at present, fully integrated in the global C balance¹¹.

Recent evidence points to the disproportionate contribution of headwater streams to the global riverine CO₂ evasion flux, because of their high cumulative length, high turbulence and tight coupling with terrestrial environments⁵,⁷. Consequently, the last few years have seen significant efforts to reduce the uncertainties on CO₂ evasion from headwater streams (for example, refs ¹²⁻²²). These studies have shed light on the temporal variability of stream CO₂ by revealing the role of hydrological variations¹²,¹⁴,¹⁵, but also diurnal cycles¹²,¹⁶, in regulating CO₂ evasion. There is also compelling new evidence to suggest that groundwater carrying soil-respired CO₂ may be a key contributor to the stream CO₂ pool¹³,¹⁴,¹⁷,²². But research on the spatial variability of these external subsurface CO₂ inputs is sorely lacking. Despite knowledge that CO₂ evasion can be a highly localized process²³⁻²⁵, very few studies have explicitly examined the dynamics of subsurface CO₂ inflows and evasion longitudinally along single streams²²,²³. Even fewer studies have attempted to capture the effect of structural heterogeneities in the stream landscape on CO₂ input and evasion rates²⁰. In this regard, we believe that current research is failing to include a substantial pathway of CO₂ input and evasion from headwater streams, most likely resulting in biased estimates of CO₂ fluxes.

Here, we outline the mechanisms of groundwater-derived CO₂ inputs in headwater catchments and explain why these inputs are likely to be a major contributor to the stream CO₂ pool. We give evidence that the enhanced delivery of CO₂ and its subsequent evasion can occur as discrete pulses and during short periods of time, making them easily overlooked by current methodologies. We also discuss why robust assessments of dominant subsurface flowpaths are required to improve estimates of the CO₂ evasion flux in headwater catchments. Lastly, we reflect on the need for hydrologists and aquatic ecologists to develop a convergent research agenda if we are to close this key knowledge gap.

## Groundwater connects terrestrial and aquatic CO₂ pools

A variety of bio-physicochemical factors can influence the balance between CO₂ source and sink terms in headwater streams. The dominant CO₂ sources in these systems are: (1) in-stream metabolism, assuming that photosynthesis rates are negligible relative to respiration rates²⁶,²⁷; and (2) inputs of groundwater carrying biogenic CO₂ (for example, refs ¹⁷,²³,²⁴). The main CO₂ sink is associated with mineral weathering, while carbonate buffering can either enhance or deplete the stream CO₂ pool²⁸. In headwater streams, sources tend to largely outweigh sinks, resulting in CO₂-supersaturated waters. While some studies report on the importance of CO₂ production via internal metabolism within the hyporheic zone¹²,¹⁸,²⁰, most other studies assume that high CO₂ concentrations are directly imputable to high rates of external, groundwater-derived CO₂. Yet, few studies have assessed the actual contributions of different CO₂ sources²⁹,³⁰. Hotchkiss et al.²⁹ showed that internal metabolism may account for only 0–19% of the CO₂ evasion flux in low-order streams of the United States. This is probably due to reduced water residence time in headwaters that do not allow significant in-stream processes to occur⁷,¹⁷.

A tight hydrological link exists between subsurface waters and stream networks. In headwater streams with limited anthropogenic

<footnote n="1">¹Research Institute for the Environment & Livelihoods, Charles Darwin University, Darwin, Australia. ²School of Environmental & Forest Sciences, University of Washington, Seattle, WA, USA. ³Department of Geography and Geosciences, Friedrich-Alexander University, Erlangen, Germany. ⁴Géosciences Environnement Toulouse, IRD, Université de Toulouse, UMR 5563, CNRS, UPS, Toulouse, France. *e-mail: clem.duvert@cdu.edu.au</footnote>
<figure><img src="image_2.png" /></figure>

**Fig. 1** | Conceptual diagram of the subsurface and stream heterogeneities contributing to CO₂ variations in headwater streams. Under wet conditions (blue curve) and assuming high terrestrial primary productivity, subsurface flowpaths connect soil CO₂ sources to streams via high-conductivity pathways (blue arrows), resulting in large CO₂ pulses along streams. Rapid evasion is favoured by in-stream geomorphic controls such as cascades or riffles causing locally turbulent conditions. Under drier conditions (pink curve), not all flowpaths are connected to streams (for example, inflow area marked ▲), while those still connected may carry lower rates of water and CO₂ (for example, inflow area marked ♦). Lower turbulence results in longer distances being needed for dissolved CO₂ to evade streams. Diffuse, low-magnitude groundwater inflow (yellow arrows) may be less significant than preferential inflow pathways in these systems.

influence, the majority of flow originates from the subsurface, may it be from saturated or unsaturated zones³¹. In fact, even during high-flow events, subsurface waters are known to contribute considerable amounts to streamflow³². These waters discharge into streams via different pathways, with varying magnitudes and rates. Where gaining-stream conditions prevail, diffuse inflow of CO₂-rich groundwater will occur along stream corridors via the hyporheic zone, contributing to a background of continual CO₂ evasion along streams. But there is increasing evidence that the hyporheic zone is not just a vent for groundwater-derived CO₂. This interface between the streambed and the subsurface can sustain high rates of organic matter decomposition, and so it has the potential to produce and deliver additional CO₂ to streamflow¹²,¹⁸,²⁰,³³. Inputs of CO₂ from the hyporheic zone can be highly variable, both in space²⁰,³³ and time¹². In-stream geomorphic heterogeneities can also enhance local infiltration of streamwater into the hyporheic zone that will then re-emerge at a downstream location, further obscuring CO₂ patterns along stream corridors.

Some subsurface inflows to the stream network are likely to be even more spatially focused. We know that headwater landscapes are often underlain by heterogeneous networks of macropores, soil pipes and cracks within weathered bedrock, and together these networks can support large fluxes of water and solutes via advective transport³⁴⁻³⁷. These subsurface conduits can ensure direct connectivity between hillslopes, riparian zones and streams, making preferential flow a dominant process both at hillslope and small catchment scales³⁷⁻³⁹. Hotspots for subsurface inflows will occur irregularly along and across stream channels, as a result of

heterogeneities in the landscape structure (for example, topographic convergence) and stream morphology (for example, changes in underlying rock, changes in streambed hydraulic conductivity due to vegetation growth causing sediment deposition, and so on). In first-order streams where discharge is commonly in the 0.001–0.1 m³ s⁻¹ range, dominant groundwater flowpaths can contribute large proportions to streamflow, sometimes even doubling the flow rate at a given point and time. Accordingly, there will be minimal dilution of the CO₂-rich subsurface waters entering the surface network, resulting in a series of irregular, high-amplitude pulses of CO₂ in the stream (Fig. 1).

## Discrete CO₂ pulses and rapid decay

The rate of CO₂ evasion from streams to the atmosphere is mainly controlled by: (1) the size of the stream CO₂ pool, which will dictate the CO₂ concentration gradient at the water-air interface; and (2) flow intensity or turbulence, which vary with streambed morphology. Headwater streams generally exhibit steep slopes and high streambed roughness that together ensure turbulent flow conditions (see ref. ⁷ and references therein). Where substantial throughputs of CO₂-rich groundwater enter the stream via preferential inflow, a steep CO₂ gradient is likely to form at the water-air interface. Turbulent conditions will cause rapid diffusion of this dissolved CO₂ into the atmosphere until CO₂ in the stream returns to atmospheric equilibrium. It can therefore be predicted that the influence of CO₂ pulses will decrease exponentially and within short distance of inflow areas, particularly where heterogeneities in stream morphology will augment turbulence, hence evasion (Fig. 1). This ‘exponential
<figure><img src="image_3.png" /><figcaption>**Fig. 2** | Illustration of CO₂ evasion within short distance of subsurface inflows. **a,** Decrease in the partial pressure of CO₂ (pCO₂) values from emerging groundwater to streams. Green, blue and brown represent tropical, temperate and boreal streams, respectively. The shaded areas around each line represent measurement uncertainties as described in the Supplementary Information. The two lines marked with green and purple asterisks in **a** and **b** correspond to data collected as part of this study in Houay Pano (Laos) and Uhlirska (Czech Republic), respectively. All other lines are taken from the literature (see Supplementary References). **b,** Decrease in flow-weighted CO₂ flux (F) from emerging groundwater to streams. Values have been normalized to the subsurface (source) CO₂ flux F₀ to facilitate inter-site comparison. **c,** Longitudinal profile of dissolved CO₂ flux along a steep tropical headwater stream in northern Laos (Houay Pano, 0.64 km²). The green curve represents the in-stream CO₂ flux with its 10th-90th percentile uncertainty range (see Supplementary Information). Yellow shaded areas represent locations of flatter reaches that support riparian vegetation with diffuse inflow of groundwater. Violin plots represent the measured CO₂ inputs delivered by preferential subsurface inflows with their 10th-90th percentile range. Black vertical dotted lines correspond to locations with higher turbulence, such as minor falls. The green asterisk refers to the data points used in **a** and **b.** **d,** Temporal variations in dissolved CO₂ flux along a temperate headwater stream in the Czech Republic (Uhlirska, 1.78 km²). Data were collected in shallow groundwater and at two stream locations, immediately downstream of a subsurface seepage area and at the outlet of the catchment, 900 m downstream of the seepage. The shaded areas around each curve represent their 10th-90th percentile uncertainty ranges. The purple asterisk corresponds to the data points used in **a** and **b.**</figcaption></figure>

decay' in stream CO₂ has been described in a number of studies (for example, refs ¹³,²⁵). Work by Johnson et al.²³ is emblematic of this mechanism, with the authors establishing that over 90% of CO₂ had outgassed within 20 m downstream of a groundwater seepage area.

The riverine fate of high-amplitude groundwater-derived CO₂ inflows remains unclear. We found a limited number of studies where dissolved CO₂ was measured both in a groundwater seepage area or spring, and in streamwater at a nearby downstream location (see Supplementary References; Fig. 2a). The compiled values, together with our data, confirm a sharp decrease in the stream CO₂ concentration and emphasize the spatially limited zone of influence of CO₂-rich inflows. Amongst these studies, only a handful weighted the CO₂ concentrations by flow data to derive a CO₂ loss rate along the groundwater-stream continuum (see Supplementary References; Fig. 2b). According to these data, the quantity of CO₂ dissolved in water would decrease by 64 to >92% in the first 100 m downstream of a groundwater seepage area (median 76%). While covering a wide range of values due to site-specific landscape controls, observed loss rates are consistent across boreal, temperate and tropical catchments and suggest that even relatively proximate in-stream measurements would miss out most of the groundwater-derived CO₂ flux. These rates should be seen as conservative

estimates of the evasion flux, because the flux measured at a given location downstream is likely to integrate other subsurface inflows along the reach, and potentially, the addition of CO₂ from other sources, thereby masking the sole effect of evasion.

Data in Fig. 2a,b are for a single subsurface inflow area, but one can envision the exponential CO₂ decay pattern to occur repeatedly along with the succession of subsurface inflows contributing to the CO₂ flux. This is illustrated with fine-scale CO₂ measurements in a headwater tropical stream and within dominant subsurface inflows along its course (Fig. 2c). Our data show several pulses of CO₂ where the stream receives subsurface water, either as diffuse inflows through relatively flat riparian corridors (yellow shaded areas) or as discrete, preferential flowpaths intersecting the stream (orange violin plots). These pulses are then followed by sudden drops where the streambed slope increases and more-turbulent flow occurs (dashed vertical lines). Such pattern repeats several times within a few hundred metres, before the stream flows into an alluvial fan 1,500 m downstream of its source. These observations imply that the evasion flux can be extremely variable along the stream, and that heterogeneities such as the presence of vegetation and decrease in flow turbulence can greatly affect it. We contend that the only likely driver of the observed CO₂ increases are the inflows of subsurface water,
**Box 1 | An integrative field toolbox to track external CO₂ inputs**

Shared methodology and cross-disciplinary expertise are needed to provide more reliable estimates of the groundwater-derived CO₂ flux and, just as importantly, to distinguish between the CO₂ delivered by subsurface inflows and that produced by in-stream metabolism. While aquatic ecologists have established robust approaches to estimate in-stream metabolism²⁷, the quantification of subsurface inflows of CO₂ is a more complex undertaking that has received much less attention, and as a result large uncertainties remain regarding their variability along streams. Here we suggest a number of avenues to close this knowledge gap.

Single-point measurements, albeit at high frequency, may not capture the complexity of headwater streams. CO₂ in particular is non-conservative and may not integrate whole-catchment processes¹⁹, and so quantifying CO₂ evasion fluxes using single-point measurements will remain fraught with uncertainty until we achieve a full understanding of the spatial variations of CO₂ within headwater streams. Accounting for spatial variability first requires delineation of groundwater inflow along stream corridors. Although one may never fully characterize the spatial heterogeneity associated with subsurface flowpaths, methods exist that can identify dominant inflow areas. Longitudinal sampling of chemical and isotopic tracers can be used for this purpose (see ref. ⁴⁵ for a review of methods), although characterization of the source is often problematic. High frequency, distributed temperature sensing can achieve finer spatial and temporal resolution of even low-magnitude groundwater inflows⁴⁶, and may be more adapted to headwater systems. This approach has also shown potential for quantifying hyporheic flow dynamics⁴⁷.

With recent developments in automated infrared CO₂ sensors, we also have the ability to investigate the dynamics of subsurface inflows and CO₂ evasion longitudinally along streams. CO₂ sensors should be combined with additional measurements of dissolved oxygen, light and temperature, so that daily and sub-daily rates of in-stream photosynthesis and

respiration can be quantified²⁷,⁴⁸. These methods generally infer a respiratory quotient of 0.85 to 1 for CO₂ production, and estimate an integrated value for net in-stream metabolism. The deviation from a stoichiometry of oxygen consumption to CO₂ production can be explored as a way to differentiate internal CO₂ production—or uptake—from external subsurface CO₂ inflows. Importantly, pH should also be monitored to yield insight into the effect of carbonate buffering on the CO₂ pool.

Also important is an appraisal of subsurface sources, and so CO₂ sensors should be installed in selected piezometers within the vicinity of streams. Geophysical methods that are sensitive to changes in hydraulic conductivity have the potential to delineate areas that are more likely to intersect preferential flowpaths⁴⁹,⁵⁰, hence more adequate for piezometer deployment. Despite the need to adequately characterize sources, we note that upscaling heterogeneous subsurface processes to entire stream lengths remains a challenge. At the catchment scale, temporal variations in the connectivity of dominant flowpaths to streams can be captured using high-frequency conductivity, chloride or, better still, water and C stable isotopic data⁵¹,⁵². With the advent of tracer-aided hydrological modelling, it is now possible to track the movement and residence time of these flowpaths over time⁵³,⁵⁴, although the role of vegetation on water partitioning is yet to be fully integrated into current models.

Finally, one promising avenue that has not yet been explored to our knowledge is to integrate temporal dynamics of high-density chemical measurements with stream network theory⁵⁵. In their current form, network models utilize empirical relationships to investigate the influence of catchment structure on the chemical composition of a stream. Incorporating temporal and physical dynamics associated with new knowledge on the role of subsurface inflows could prove fruitful to quantify the relationships between stream structure and CO₂ fluxes.

rather than internal metabolism, because of very short water residence times due to moderate to steep slopes across the entire stream length (average 0.14 m m⁻¹), as well as a largely shaded stream corridor less favourable to heterotrophic metabolism. While not all headwater streams originate in forested systems, and lower-gradient, open-water systems may have important in-stream primary production, we posit that subsurface inputs and geomorphic heterogeneities are the largest control on small-scale, high-amplitude variations in headwater stream CO₂ fluxes.

Based on a mass balance approach that uses both subsurface and stream CO₂ measurements (see Supplementary Information), we calculated a catchment-wide evasion flux of 72 g C ha⁻¹ d⁻¹ (10th–90th percentile range 47–102 g C ha⁻¹ d⁻¹). It is noteworthy that widely used empirical models⁴⁰ would largely overestimate the evasion flux, with predictions ranging between 179 and 789 g C ha⁻¹ d⁻¹ (models 2 and 5; 10th–90th percentile ranges 139–224 and 622–950 g C ha⁻¹ d⁻¹, respectively). Such a large discrepancy between measured and modelled values corroborates findings from other authors that more data is needed to validate these models for steep catchments⁴¹.

**Hydrological connectivity as a driver of CO₂ variability**

In addition to the extreme spatial variability of subsurface inflows along headwater streams, the magnitude and rate of CO₂ inputs may also be highly dynamic at both seasonal and event scales (Fig. 1). In temperate environments, high rates of primary productivity generally coincide with warmer weather and lower-flow conditions, hence high groundwater-derived CO₂ flux in the stream may not

always lead to high riverine CO₂ evasion due to lower flow intensity²². This decoupling between CO₂ input and evasion may not hold for tropical environments, where high-flow conditions and high primary productivity typically occur concomitantly.

At the event scale, not all pulses of precipitation may result in the flushing of dissolved CO₂ from the subsurface into streams. The exceedance of a storage threshold is often needed for the initiation of preferential flowpaths in the subsurface⁴². Because shifts in hydrological regime may temporarily (dis)connect dominant flowpaths to streams, shallow groundwater may act as a temporary CO₂ sink when it is not fully connected, and as a CO₂ source following flowpath initiation (Fig. 1). To illustrate this, we present a time series of dissolved CO₂ collected along a snowmelt-dominated headwater stream of the Czech Republic (Fig. 2d). We show that a large snowmelt event in April induces a short-lived CO₂ pulse in the vicinity of a groundwater seepage area, which we interpret as the release of previously trapped soil CO₂ following infiltration of snowmelt waters—the snow cover acting as an insulant during winter (for example, ref. ⁴³). This large CO₂ pulse was not detected a few hundred metres downstream, because of enhanced evasion along the stream reach.

Evasion flux estimates based on empirical models range between 13 and 30 g C ha⁻¹ d⁻¹ (these two values corresponding to models 5 and 7, with 10th–90th percentile ranges 10–16 and 23–38 g C ha⁻¹ d⁻¹, respectively) and are in reasonable agreement with our mass balance (24 g C ha⁻¹ d⁻¹; 10th–90th percentile range 22–26 g C ha⁻¹ d⁻¹). However, the latter may underestimate the true evasion flux as we have no intermediate measurement site along the 900 m stream
reach, and so other CO₂ inputs may have been overlooked. While the empirical models may be better adapted to streams located in temperate areas and with gentler slope, such as the one studied here (average slope 0.02 m⁻¹), we note that the models again yield large uncertainties and, more concerningly, lack consistency among them (see Supplementary Information).

The relationship between water movement in the subsurface and CO₂ delivery to streams is poorly understood. Different flowpaths may transport different quantities of CO₂ originating from different sources, and these may vary with varying hydrological conditions⁷. Despite being connected to streams only during short-lived high-flow events, shallow preferential flowpaths may be mobilizing the majority of terrestrially derived CO₂. For instance, episodic water table rise was found to trigger CO₂ release to a stream preferentially through a thin layer of riparian soil¹⁴. Shallow flowpaths can also displace older, stored waters that have had time to equilibrate with the CO₂-enriched subsurface environment. Large stream CO₂ fluxes observed shortly after rainfall events were attributed to the activation of shallow flowpaths carrying a mixture of these older waters and more recent stormwater¹⁴. By contrast, deeper flowpaths may be less prone to temporal variations and sustain baseflow—and CO₂—to streams more consistently. In carbonate-dominated catchments, these flowpaths will probably deliver to streams some CO₂ of geologic origin, and understanding the relative contribution of geogenic CO₂ is also critical for balancing catchment C budgets.

## Need for a concerted effort that bridges disciplines

The non-linear behaviour of subsurface flow is well recognized across the hydrological community, while aquatic ecologists understand the biogeochemical mechanisms that influence C chemistry. We suggest that to achieve informed and quantitative estimates of the role headwater streams play for landscape-scale C cycling, these two communities must combine efforts (Box 1). Closer collaboration and the adoption of a systematic observational approach across sites covering a range of biogeoclimatic regions, will pave the way for a better inclusion of groundwater-derived CO₂ in catchment C budgets. In particular, delineating and quantifying water sources and their residence times in the subsurface will assist us in understanding when, where and how much CO₂ is delivered to streams, while at the same time taking the necessary steps to identify the influence of in-stream metabolism on C cycling.

We reveal the spatial and temporal variability of CO₂ delivered by groundwater and that emitted to the atmosphere. We show that in-stream CO₂ fluxes are enhanced where and when structural hotspots and hydrological hot moments overlap, creating the conditions for disproportionately high rates of CO₂ evasion. This extreme variability suggests the potential misinterpreting of CO₂ emissions at the catchment scale. Clarifying the mechanisms and controls underlying the processes of CO₂ input and evasion is now needed to better understand riverine C cycling.

Received: 16 January 2018; Accepted: 14 September 2018; Published online: 29 October 2018

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## Acknowledgements

We acknowledge funding from the Australian Research Council (DP160101497), the German Research Foundation (project 718 BA 2207/10-1) and the French Institut de Recherche pour le Développement. D.E.B. was partially supported by a NASA Carbon Cycle Science grant (NNX17AI74G). We thank M. S. Johnson, J. B. Shanley and D. H. Doctor for sharing important site information and data, and J. A. C. Barth for insightful comments on an earlier version of the manuscript. This paper also benefited from discussions with M. I. Bird, M. Rudge and R. T. Barnes. We acknowledge the Lao Department of Agricultural Land Management and the M-TROPICS observatory for access to the Houay Pano site, as well as the Czech Geological Survey for access to the Uhlirska site. N. Silvera, K. Latsachack, J.-P. Thiébaut, K. Xayyathip, M. Sanda, J. Jankovec and A. Kulasova are thanked for fieldwork assistance.

## Author contributions

C.D. conceived the analysis and carried out the literature review and data analysis. D.E.B. contributed to the conceptual development of the manuscript, data analysis and presentation. L.B.H. was involved with discussions particularly during early stages of the manuscript. A.M. collected the 'Uhlirska' dataset and contributed to data analysis. O.R. and C.D. collected the 'Houay Pano' dataset. C.D. wrote the first draft and all authors edited and commented on various iterations of the manuscript.

## Competing interests

The authors declare no competing interests.

## Additional information

**Supplementary information** is available for this paper at https://doi.org/10.1038/s41561-018-0245-y.

**Reprints and permissions information** is available at www.nature.com/reprints.

**Correspondence** should be addressed to C.D.

**Publisher's note:** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

© CROWN 2018
Methods

**Data collection.** At Houay Pano (Laos), 64 stream locations and 10 subsurface inflows were sampled along the main watercourse in May 2005, under low-flow conditions (pre-monsoon). Temperature and pH were measured at each location using WTW portable sensors. Samples were filtered through 0.45 µm and analysed by acid titration within 48 hours for total alkalinity, following the Gran method⁶⁶. All *pCO₂* values were calculated from total alkalinity, pH and temperature measurements according to carbonate equilibria in freshwater⁷³. Discharge measurements were conducted at each accessible site using NaCl and a dilution-gauging approach. Each chemical gauging was repeated three times. Further details on the morphology and hydrology of the Houay Pano catchment can be found in refs ⁵⁸,⁵⁹. At Uhlirska (Czech Republic), streamwater was collected at two locations on a daily to monthly basis and for over a year (2015), while shallow groundwater was collected from four boreholes adjacent to the stream on a monthly basis during the same period. Groundwater samples were collected 24 hours after purging the boreholes using a peristaltic pump. Temperature and pH were determined in the field with a HACH multi-parameter device, while samples were taken for later determination of dissolved inorganic carbon (DIC) using an OI Analytical Aurora 1030W TIC-TOC analyser⁶⁰. All *pCO₂* values were calculated from DIC, pH and temperature measurements as detailed in ref. ⁶⁰. Stream discharge was determined using a V-notch weir and a pressure sensor at each of the two stream locations. The upstream site (POR) represents the outflow of a large groundwater seepage area, while the downstream site (UHL) is located at the outlet of the catchment, 900 m downstream of the groundwater seepage area. Further details on the Uhlirska catchment are available in refs ⁶⁰,⁶¹.

**Empirical models.** We first estimated the CO₂ evasion flux for each of the two study catchments based on empirical relationships from the literature. Water-air gas transfer velocities (*k*) were derived from physical variables (average streamed slope, depth, flow velocity, water temperature) using existing models⁶⁰. Out of the seven regressions established by Raymond et al.⁶⁰, models 1, 2, 5 and 7 were chosen because they are likely to provide more robust estimates⁶⁰. For Uhlirska, velocity estimates were calculated from hydraulic geometry coefficients, while for Houay Pano flow velocities were measured in the field together with discharge. All *pCO₂* values measured at the outlet of a given catchment at time *t* were converted into CO₂ concentrations *C*, using Henry's temperature-dependent constant⁶², and the area-specific CO₂ evasion flux *F* was computed as:

$$F = \sum_{t} k_{t} (C_{t} - C_{\text{atm}})$$

where *C*<sub>atm</sub> is the atmospheric CO₂ concentration, assumed to be constant at 400 ppm. We calculated *F* based on one set of measurements for Houay Pano (*t* = 1), while our entire time series was integrated for Uhlirska. Error ranges were obtained with a Monte-Carlo approach, each model input parameter being randomly selected over their domain as given by Raymond et al.⁶⁰. Discharge and *pCO₂* measurements were also randomly generated from a Gaussian distribution centred on the measured value and with relative standard deviation ±21% for *pCO₂* and ±15% for discharge. Uncertainties were then propagated to evasion estimates. We ran 10,000 simulations for each model (Supplementary Fig. 1) and report all uncertainties in the main text as the 10th–90th percentile ranges. All data analyses were performed with MATLAB R2017a.

**Mass balance.** Our mass balance approach is based on spatial iterations of the upstream-to-downstream decreases in CO₂ concentrations along the main watercourse. Using discharge measurements and a differential gauging approach, we derived dissolved CO₂ fluxes for each stream reach as well as for entering groundwater (Supplementary Fig. 2). Importantly, no significant tributary inflow was observed along the main streams, so that the groundwater inflow rate between adjacent stream locations could be estimated relatively accurately using our incremental discharge measurements. For each stream reach *x*, the evasion term *f* was obtained according to:

$$f_x = -\frac{\partial}{\partial x} CQ + (C_{gw}Q_{gw})_x \text{ with } Q_{gw,x} = \frac{dQ}{dx}$$

where *C* and *Q* (stream) and *C*<sub>gw</sub> (subsurface) were measured and *Q*<sub>gw</sub> was calculated by differential gauging. The total evasion flux *F* was then obtained as:

$$F = \sum_{t} \sum_{x=1}^{n} f_{x,t}$$

where *n* is 2 and 64 for Uhlirska and Houay Pano, respectively. At Uhlirska, the entire time series was integrated over *t* to obtain a total flux over the study period, which was then normalized per day. At Houay Pano, linear interpolations between closest stations were used to derive discharge data for stream locations where we were not able to measure discharge directly. In addition, for stream reaches where groundwater CO₂ data were not available, we used the concentration obtained from the closest station upstream. At Uhlirska, groundwater CO₂ concentrations were

derived from the average of four shallow boreholes, and linear interpolations were used to derive values for the dates without measurement.

Uncertainties once again were quantified by means of 10,000 Monte-Carlo simulations, where at each stream location, discharge and *pCO₂* measurements were randomly generated from a Gaussian distribution centred on the measured value and with relative standard deviation ±21% of measured *pCO₂* and ±15% of measured discharge. Uncertainties were then propagated to evasion estimates based on the mass balance detailed above. Supplementary Fig. 3 presents the distribution of evasion estimates for the two sites, as well as a comparison with modelled estimates. We chose a conservative error range (±15%) for discharge measurements⁶³, given that dilution-gauging measurements were repeated three times and averaged in Houay Pano, and that V-notch weirs and consistent stage-discharge rating curves were used in Uhlirska. A conservative relative standard deviation was also preferred for *pCO₂* calculations (±21%), based on a pH measurement uncertainty of ±0.1 pH units⁶⁰.

**Data from the literature.** We reviewed the literature with an aim to select studies where *pCO₂* was measured both in a groundwater seepage area or spring, and in streamwater at a nearby downstream location. Because the ultimate goal was to assess the CO₂ evasion flux from emerging groundwater to the stream, we only included studies where the subsurface inflow rate was contributing most flow, if not all, to the downstream measurement location. In doing so, we had to exclude studies where dilution effects were evident between, for instance, a measure within the hyporheic environment and another measure in overlying streamwater¹²,¹⁸. We also discarded studies that did not explicitly characterize a subsurface- stream continuum, with potential decoupling between groundwater and stream measurements¹⁵,⁶⁴,⁶⁵. Lastly, studies where the distance between groundwater and stream measurements was not clearly specified were also discarded⁶⁶,⁶⁷. We found 12 studies¹⁴,²²,⁴⁸,⁶⁶⁻⁷⁵ that conformed to our criteria, of which 9 also had flow data (Supplementary Table 1). We augmented the obtained dataset with new data from three sites—Houay Pano, Uhlirska and Howard Spring in tropical Australia.

While in a few studies discharge was measured only at the upstream site (for example, refs ⁶⁹,⁷⁰), all observed flow was reported to originate from a single high-magnitude groundwater spring, and so we could reasonably assume that the flow rate measured at the spring did not change significantly downstream. Because our purpose was solely to document in-stream CO₂ losses, we did not distinguish between sites where the origin of CO₂ was likely to be geogenic (for example, ref. ⁷⁰) to those where CO₂ was biogenic (for example, ref. ²³). For sites with repeated measurements, we deliberately picked the highest evasion rate between upstream and downstream sites, for example, for Uhlirska, the short-lived snowmelt event with largest CO₂ loss (Fig. 2d). Confidence intervals were obtained using the *pCO₂* measurement error as specified in each individual study. For discharge measurements, we considered a relative standard deviation of ±15%, which we propagated to our evasion flux estimates (Fig. 2b). Lastly, all CO₂ fluxes were normalized by their upstream CO₂ flux (*F*<sub>0</sub> in Fig. 2b) to obtain comparable per cent loss rates across sites.

Data availability

The data that support the findings of this study are available from the corresponding author upon request.

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