CO₂ dynamics along Danish lowland streams: water–air gradients, piston velocities and evasion rates

Abstract

We measured CO₂ concentration and determined evasion rate and piston velocity across the water–air interface in flow-through chambers at eight stations along two 20 km long streams in agricultural landscapes in Zealand, Denmark. Both streams were 9–18-fold supersaturated in CO₂ with daily means of 240 and 340 μM in January–March and 130 and 180 μM in June–August. Annual CO₂ medians were 212 μM in six other streams and 460 μM in four groundwater wells, while seven lakes were weakly supersaturated (29 μM). Air concentrations immediately above stream surfaces were close to mean atmospheric conditions except during calm summer nights. Piston velocity from 0.4 to 21.6 cm h⁻¹ was closely related to current velocity permitting calculation of evasion rates for entire streams. CO₂ evasion rates were highest in midstream reaches (170–1,200 mmol m⁻² day⁻¹) where CO₂-rich soil water entered fast stream flow, while rates were tenfold lower (25–100 mmol m⁻² day⁻¹) in slow-flowing lower reaches. CO₂ evasion mainly derived from the input of CO₂ in soil water. The variability of CO₂ evasion along the two lowland streams covered much of the range in sub-Arctic and temperate streams reported previously. In budgets for the two stream catchments, loss of carbon from soils via the hydrological cycle was substantial (3.2–5.7 mmol m⁻² day⁻¹) and dominated by CO₂ consumed to form HCO₃ ⁻ by mineral dissolution (69–76%) and export of organic carbon (15–23%) relative to dissolved CO₂ export (7–9%).

Introduction

Streams are usually supersaturated with CO₂ due to inflow of CO₂-rich soil water and predominance of respiration relative to photosynthesis due to degradation of organic matter received from land (Kelly et al. 1983; Sand-Jensen et al. 1995; Battin et al. 2008). Extensive CO₂ supersaturation supports photosynthesis and growth of numerous amphibious plants which are unable to use HCO₃ ⁻ for photosynthesis (Sand-Jensen et al. 1992; Sand-Jensen and Frost-Christensen 1998). Extensive CO₂ supersaturation of turbulent stream water should also lead to substantial evasion to the atmosphere of CO₂ originally derived from the soil as CO₂ or degradable organic matter. This loss is seldom included in budget calculations of soil CO₂ loss (Sand-Jensen et al. 2007). Moreover, in studies of local, regional and global carbon cycles, the rapid CO₂ exchange with the atmosphere in the turbulent stream flow has rarely been measured directly and included in a wider CO₂ flux perspective. Our overall objective was to evaluate the magnitude of CO₂ evasion from streams in a carbon flux perspective for the stream and the catchment.

Evasion of CO₂ to the atmosphere is highly variable temporally and spatially due to the complexity of hydrological, biological and physical processes determining the gradient and exchange coefficient (piston velocity) of CO₂ from water to air (Hope et al. 2001; Worall and Burt 2005). High evasion rates have been reported from turbulent upper reaches of streams draining temperate forests and peat land while evasion rates are 5–15 times lower in deeper downstream reaches of lower turbulence and CO₂ concentration (Hope et al. 2001; Silvennoinen et al. 2008). This difference shows the importance of CO₂ supply in soil water and contact time with the atmosphere for evasion rates along the streams. To confirm the magnitude of estimated evasion rates derived indirectly from general hydraulic formulae or use of trace gases, direct measurements are needed. Our second aim was to analyze daily and seasonal variations in CO₂ supersaturation along two lowland Danish streams in fertile agricultural landscapes and measure CO₂ evasion rates directly in flow-through flux chambers. This approach can constrain the true variability of evasion rates within and among streams and provide integrated values for entire streams that can be used in mass balances of the external terrestrial and internal stream sources of CO₂ to atmospheric release.

We calculated piston velocity directly from measurements of evasion rates and gradients of CO₂ across the air–water interface using flux chambers and tested the relationship of piston velocity to common hydraulic parameters (e.g. current velocity, water depth, and stream slope) known to influence surface turbulence (Thyssen and Erlandsen 1987; Sand-Jensen and Pedersen 1999). Near-surface turbulence drives the exchange of gases across the water–air interface (Jähne et al. 1987; Wanninkhof et al. 2009), but many individual processes can influence surface turbulence and gas transfer; for example, surface renewal (Komori et al. 1993), surface penetration (Atmane et al. 2004), surface divergence (Turney et al. 2005) and thickness of the near-surface layer (Harriott 1962). Mechanistic approaches attempting to describe the turbulence have so far had limited applicability (Zappa et al. 2007; Vachon et al. 2010). A formula relating piston velocity to turbulent dissipation rate to the 1/4 power has some predictive power for rivers, estuaries and oceans combined (Zappa et al. 2007), but its application requires measurements with advanced Doppler velocimeters and improved prediction of piston velocity to ensure reliable calculations of evasion rates (Vachon et al. 2010). Estimates of piston velocity for CO₂ derived from measurements on trace gases still suffer from limited replication and uncertainties when converted to CO₂ (Genereux and Hemond 1992; Raymond and Cole 2001). This is an important problem because CO₂ reacts with water and water vapor (Ho et al. 1997) and reactions and transport depend on pH, temperature and organic surface films (Frew 1997) in ways that may differ from those of other trace gases. Moreover, correct determination of evasion rate requires knowledge of both piston velocity and the CO₂ gradient across the water–air interface and, thus, direct CO₂ measurements in water and air are needed anyway.

The CO₂ concentration above the water surface is usually assumed to be equal to the mean level in the atmosphere. This assumption has rarely been tested and it is violated if CO₂ accumulates in stagnant air receiving a high CO₂ flux from supersaturated waters below. This situation may arise in small, wind-protected streams receiving CO₂-rich soil water. Our final objective was to test whether CO₂ does accumulate in air above CO₂-rich small streams and how it influences the CO₂ gradient and the evasion rate.

Methods

Study sites

Pøle and Havelse are two small lowland streams located in an open calcareous moraine landscape in North Zealand, Denmark (Fig. 1; Sand-Jensen et al. 2007). The Pøle stream is 21 km long and drains 92 km² of mixed agricultural (57%), urban (30%) and forested (13%) area. Pøle stream receives purified treated sewage (mechanically, biologically, and chemically) from the large town of Hillerød (35,000 inhabitants). The percentage of lakes is about 1% of the Pøle catchment. Including the large Lake Arresø (38 km²) located downstream of Pøle stream raises the percentage to 22. The Havelse stream is 22.6 km long and drains 130 km² of mixed agricultural (85%), urban (10%) and forested (5%) area and receives chemically and biologically purified sewage from small villages (about 5,000 inhabitants). The Havelse catchment is devoid of lakes.

Fig. 1

Map over North Zealand, Denmark showing the location of the two streams, Pøle and Havelse with sampling sites and the largest cities and beech forest in the otherwise agricultural landscape

Eight stations were located equidistantly along the length of the Pøle and the Havelse streams. The uppermost stations in the Pøle stream (P1 and P2) and the Havelse stream (H1 to H3) were very shallow (mean depth <0.2 m) and narrow (mean width <1.5 m). The lowermost station in the Pøle stream (P8) was 9.7 m wide and 0.9 m deep, while the lowermost station in the Havelse stream (H8) was 6.6 m wide and 0.5 m deep. Both streams are channelized, have relatively uniform depths and the banks are without trees but support tall emergent herbs during summer offering shading and wind protection.

The annual average discharge for the last 30 years is similar for both streams; 26.5 for Pøle and 24.7 10⁶ m³ for Havelse (Frederiksborg 1996). High discharge and low surface irradiance during winter reduce aquatic plant growth while substantial growth of benthic microalgae and submerged macrophytes takes place in May–August (Sand-Jensen et al. 1988; Sand-Jensen and Frost-Christensen 1998). Daily mean discharge and water depth and transversal depth profiles across the stream were available for six hydrometric stations in the Pøle stream (P3–P8) and three stations in the Havelse stream (H3, H5 and H7) continuously operated by the county for more than 30 years (unpublished reports from Frederiksborg Amt). This information permitted calculation of daily mean current velocity (U, m s⁻¹) throughout the year as daily mean discharge (Q, m³ s⁻¹) divided by daily mean transversal area (A, m²), i.e. U = Q A⁻¹. Discharge, water depth and current velocity at the remaining stations were estimated by measuring the hydraulic parameters twice a month, establishing close relationships to hydrometric stations nearby and estimating the daily hydraulic parameters from these relationships. Oxygen consumption of the input of easily degradable organic matter (BOD) over 24 h is expected to take place within the streams and these rates were measured at the same eight stations along both streams at monthly intervals and converted to CO₂ release using a molar quotient of CO₂ to O₂ of 1.0 (Pedersen 2004).

To obtain an overall picture of the regional freshwater CO₂ concentration we performed year-round measurements during 1999 at several stations arranged equidistantly along six other streams, in the outlet from seven large eutrophic lakes, in four groundwater wells and in soil water leaving the drain pipes (Sand-Jensen et al. 1995). All localities were within 30 km from the town of Hillerød. The median CO₂ concentration in groundwater was 460 μM (88% of 133 measurements were between 320 and 640 μM, see later) and concentrations in drain water were at the same level for the same average bicarbonate alkalinity as in the streams (4,500–5,500 μeq l⁻¹, Sand-Jensen et al. 2007). This agreement was anticipated due to the equilibrium of calcite dissolution by CO₂ in carbonate-rich soils (Dreybrodt 1988). Silicate weathering only contributes ~10% to HCO₃ ⁻ formation in the soils, while 90% derive from dissolution of carbonates (unpublished data). In the dissolution of silicate in the soil one CO₂ molecule is produced for every HCO₃ ⁻ molecule formed and in the dissolution of carbonates one CO₂ molecule is consumed for every two HCO₃ ⁻ molecule formed permitting determination of total CO₂ loss from the soils to the streams in dissolved CO₂ and HCO₃ ⁻ (Sand-Jensen and Staehr 2007). Including loss of terrestrial organic carbon to the streams (Pedersen 2004) permits construction of carbon budgets on a catchment scale.

CO₂ concentration, evasion rate and piston velocity

The CO₂ concentration was determined about monthly at all 16 stations over 1 year by measuring pH, alkalinity, temperature and conductivity in water samples collected just before noon (10.00–12.00) following standard methods (Mackereth et al. 1978; Sand-Jensen and Frost-Christensen 1998).

Air concentrations of CO₂ at 2 m above the stream surface were measured with a portable infrared gas analyzer (IRGA; LCA-3, Analytical Development Company, England) during daytime measurements of CO₂ evasion with a flow-through chamber (see below). Air CO₂ concentration was measured with greater spatial and temporal resolution during a calm summer night and day in a 4 m wide mid-stream station (P4) in the Pøle stream. Air samples were collected using PVC pipes (3 m long, 0.5 cm in diameter, and perforated with small holes) mounted horizontally 1, 2 and 4 cm above the stream. Air was sucked at a rate of 140 ml min⁻¹ through air-tight tubing by a pump in the IRGA. Wind velocity was measured 2 m above the water surface using a Hobo anemometer.

CO₂ evasion from supersaturated stream waters was determined in repeated measurements from sunrise to the afternoon between June and November at 9 mid-stream and downstream stations in the Pøle (P4–P8) and the Havelse stream (H3–H8) representing the largest surface areas and emission rates from the streams. A full daily measurement program was performed at every station on three occasions in June–July, August–September and October–November. To save time, measurements were not performed at the most upstream stations because flow conditions here resemble those at mid-stream stations and piston velocity and CO₂ evasion rate can be calculated from measured current velocity and CO₂ concentration. Also, upstream stations are narrow and contribute less to the integrated stream evasion of CO₂ than wider stations further downstream. Measurements of evasion rates in the streams covered most of the range in water depths (0.09–0.90 m) and current velocity (0.01–0.82 m s⁻¹) that is observed at the stream reaches over the year.

Measurements were made with a flux chamber which sealed off 19.1 dm³ (V_ch) of atmospheric air above 11.68 dm² (A_ch) of stream surface area (Fig. 2). The accumulation of CO₂ in the enclosed air volume was measured with the IRGA while maintaining unaltered stream flow and turbulence. The rationale for construction and use of the chamber is that gas piston velocity (K_L) in these shallow and narrow streams is regulated by surface turbulence (Zappa et al. 2007) which, in turn, is determined by turbulence in the streaming water generated by current velocity and roughness elements at the bottom and along the banks. Wind exposure is small and its influence on surface turbulence and piston velocity is insignificant (Moog and Jirta 1999; Raymond and Cole 2001). Likewise, piston velocity of oxygen in small streams was predicted previously from hydrological parameters (e.g., current velocity, water depth and energy gradient; Thyssen and Erlandsen 1987; Thyssen et al. 1987).

Fig. 2

Sketch of flux chamber made of a half-cylinder of gas-tight Perspex which is aligned with the flow, placed with the side walls 1 cm below the water surface and sealed by plastic flaps from the end walls floating on the water surface. Air within the chamber is circulated via a continuously measuring CO₂ analyzer

The flux chamber was a half-cylinder 94 cm long and 18 cm in internal diameter made of gas-impermeable PVC painted white to prevent heating (Fig. 2). The chamber has end-walls that are 2 cm shorter than the chamber walls and are supplied with 4 cm long skirts of thin flexible plastic that rest on the water surface in the direction of flow and form a gas tight seal (Christensen 2000). The chamber was placed with the main axis oriented in the flow direction and the lower 1 cm under water. Thus, the maximum height of enclosed air was 8 cm. The chamber had two 120 cm long iron pegs glued to the outer wall and rested on iron pegs placed transversally across the stream. The transversal pegs were connected to vertical pegs bored into the sediment well away from the chamber to avoid interference with the flow. The height of the transversal pegs was adjusted such that the chamber side walls extended exactly 1 cm below the water and the plastic skirts of the end walls rested on the water surface.

The inlet and outlet of the IRGA was connected to the air volume in the chamber via air-tight tubing. Gas was circulated at a rate of 600 cm³ min⁻¹ and gas movements were sufficient to keep the chamber air mixed and ensure a linear rise in CO₂ concentration over time. The CO₂ concentration was analyzed every 10 s over 150 s and the linear rise based on 16 data points (α, μl CO₂ l⁻¹ atmospheric air s⁻¹) was used to determine the CO₂ flux (F_A, mol CO₂ m⁻² h⁻¹) according to

$$ \;{\text{F}}_{{{\text{A}}\;}} { = }\;{{\upalpha}}\;{\text{V}}_{\text{ch}} {\text{f}}\;{\text{V}}_{{{\text{CO}}_{ 2} }} \; ( {\text{temp)}}^{{{ - 1}\;}} {\text{A}}_{\text{ch}}^{ - 1} $$

(1)

where f converts flux rates from seconds to hours and from dm² to m² and V_CO2 (temp) is the volume of 1 mol of CO₂ at the actual temperature and one atmosphere. Pressure changes are small and can safely be neglected. V_CO2 (temp) was corrected according to

$$ {\text{V}}_{{{\text{CO}}_{ 2} }} \; ( {\text{temp)}}\;{ = }\;{\text{V}}_{{{\text{STP}}\;}} ( {\text{Temp}}\;{ + }\; 2 7 3. 1 5 )\; ( 2 7 3. 1 5 )^{ - 1} $$

(2)

where V_STP is 22.258 l CO₂ mol⁻¹ at 0°C and one atmosphere and Temp is the actual temperature in °C (Waser et al. 1982).

Piston velocity (K_L, m h⁻¹ = 100 cm h⁻¹) was calculated from flux measurements (F_A, mol m⁻² h⁻¹) and the concentration difference of CO₂ between water and air (Thyssen et al. 1987)

$$ {\text{K}}_{{{\text{L}}\;}} { = }\;{\text{F}}\; ( {\text{CO}}_{ 2}^{\text{mea}} \; - \;{\text{CO}}_{ 2}^{\text{equ}} )^{ - 1} $$

(3)

where CO ^mea₂ is the actual CO₂ concentration dissolved in the water calculated from continuous measurements of pH, conductivity and temperature (YSI-multisonde, 600 XL-100-0) and acidimetric Gran titration of total dissolved inorganic carbon (DIC) in water samples retrieved every 30 min and analyzed following Mackereth et al. (1978). CO ^equ₂ is the concentration of CO₂ in water in equilibrium with the measured CO₂ concentration in the air 2 m above the stream surface. The air concentration was measured approximately every 20 min. CO ^equ₂ is calculated from the measured air concentration and Henry’s constant corrected for the influence of temperature (Maberly 1996).

Measuring range of the IRGA was 0–1,600 μl CO₂ l⁻¹ and measuring accuracy was ±0.5 μl CO₂ l⁻¹. Calibration was made by manufactured gases of known concentration. A total of 200 triplicate flux measurements (i.e. 600 single flux measurements) were made. Coefficients of determination (r ²) based on linear regression of CO₂ concentration versus time in the flux experiments averaged 0.99. Triplicate determinations of piston velocity were highly reproducible with an average CV (SD/mean) of only 5.3% in 200 series.

Measurements at each reach were performed from before sunrise to the afternoon at one to four positions of the flux chamber depending on physical heterogeneity across the stream. In wide, heterogeneous streams, the surface was divided into a near-bank section and a mid-stream section of equal sizes and two positions were selected in the middle of the two. Metal frames to support the flux chamber were set up at all positions and the chamber was moved between these positions such that 3–8 triplicate measurements were made at each position over the day. Current velocity was measured in replicate over 1 min at a position 0.5 m upstream of the flux chamber during each measurement series. Water depth was the mean of measurements at positions along the sides, upstream and downstream of the chamber. Piston velocity for an entire reach was calculated as the mean value of all piston velocities determined at different local sites and periods for an entire day. The mean slope of the water surface along the reach (m km⁻¹) was measured by filling a 12 m long flexible, transparent plastic tube with water and measuring the difference in hydraulic head between the downstream open end of the tube relative to the water surface with an accuracy of 1 mm. Mean current velocity over a 50 m reach was measured as the passage time of 50% of an added quantum of NaCl dissolved in 20 l of water. Salt passage was followed by continuously logging conductivity downstream of the reach. Mean depth was calculated from measurements at 25 cm intervals across 11 transversal sections placed 5 m between each other along the reach.

The predictive relationships between piston velocity and hydraulic parameters were established for piston velocities at 20°C (K ²⁰_L ). Temperature correction from ambient temperature (K ^amb_L ) to 20°C was performed according to Thyssen and Erlandsen (1987)

$$ {\text{K}}_{\text{L}}^{\text{amb}} \;{ = }\;{\text{K}}_{\text{L}}^{ 2 0} \; ( 1. 0 2 4^{{ ( {\text{amb}}\;{ - }\; 2 0 )}} )\; $$

(4)

The annual integrated evasion rates for entire streams were estimated from measured mean monthly CO₂ concentrations and water temperatures at eight stations along the streams and mean piston velocity estimated from mean monthly current velocity and temperature at the same stations. The established empirical relationship between piston velocity and current velocity (see later in Table 2, line 1) and the temperature correction in Eq. 4 were used to calculate piston velocity. Stream surface areas between stations were calculated from measured stream width and distance between stations.

Net photosynthesis was measured between 9.00 and 13.00 during flux measurements according to Odum’s single station method (Odum 1956). Dissolved oxygen in the water was recorded continuously (YSI, 600XL-100-0) and atmospheric exchange was calculated using Eq. 3 by substituting oxygen for CO₂ and converting measured piston velocity for CO₂ to oxygen following Thyssen and Kelly (1985).

Results

CO₂ concentration in air

During measurements with the flux chamber, the mean CO₂ concentration in the air at 2 m was 352 μl l⁻¹ corresponding to equilibrium concentrations in Pøle stream of 16.2 ± 2.7 μM (SD, n = 495), while air and equilibrium concentrations were slightly higher in Havelse stream (17.0 ± 1.8 μM, n = 305). At wind-protected reaches with tall herbs on the banks, the air concentration had risen in the night and early morning on five of 24 occasions to 1.3–2.0 times above the typical atmospheric level (i.e. 20.0–31.9 μM in water at air equilibrium). These locally elevated air concentrations declined within 1–2 h when solar heating induced a weak wind (Fig. 3).

Fig. 3

Diurnal changes in CO₂ concentration measured in the air 1 cm (open circle), 2 cm (filled circle), 4 cm (open triangle) and 2 m (filled triangle) above the water surface (upper) and wind speed measured at 2 m (lower)

CO₂ at four vertical levels in the air during a very calm summer night rose to 580 μl l⁻¹ at 1, 2 and 4 cm above the water surface, while CO₂ rose to 500 μl l⁻¹ at 2 m (Fig. 3). Elevated CO₂ disappeared at low wind speeds in the morning (<0.2 m s⁻¹) and had a limited impact on CO₂ fluxes because they coincided with peak CO₂ concentration in the water (145–590 μM). The water–air CO₂ gradient was at most reduced by 11% due to CO₂ accumulation in still air and delayed CO₂ evasion for only 1–2 h.

CO₂ concentration in water

CO₂ was greatly supersaturated at all eight stations in both streams throughout the year (Fig. 4). The uppermost station in Pøle stream (P1) received soil water from fields and a refuse dump and had particularly high HCO₃ ⁻ and CO₂ concentrations (annual median 1490 μM CO₂). CO₂ concentration became significantly lower (annual median 115 μM at P6 and P7) at the relatively wide and shallow midstream reaches conducive to CO₂ evasion and photosynthesis. CO₂ concentration increased (median 170 μM) and became less variable towards the mouth of Pøle stream (P8), which has deeper slow-flowing water that restricts CO₂ evasion. CO₂ concentration changed less along the Havelse stream, but as in Pøle stream, it was slightly higher at upper and lower reaches than at mid-stream reaches (Fig. 4). Over the year, median CO₂ concentration was highest in winter (Havelse = 210 μM; Pøle = 430 μM; Fig. 4) and lowest in mid-summer (Havelse = 116 μM; Pøle = 171 μM) because input of CO₂-rich soil water was higher and photosynthetic CO₂ consumption lower in winter than in summer.

Fig. 4

CO₂ concentration at eight stations in the Pøle (upper panel) and Havelse streams (lower panel) in winter (January–March), spring (April–May), summer (June–September) and autumn (October–December). Data are means of 2 or 3 monthly measurements

Downstream decline of CO₂ concentration can be explained by the increased retention time of supersaturated water in the stream which facilitates release to the atmosphere, while net photosynthesis did not change significantly along Pøle stream (r = −0.46, P = 0.44) and Havelse stream (r = 0.75, P = 0.25). CO₂ loss to the atmosphere from a given stream water volume and unit time is given by the concentration difference multiplied by the time-specific piston velocity (K₂ = K_L H⁻¹, where H is mean water depth). K₂ declined during summer to almost zero in the deeper, lowermost reaches (P8 and H8: 0.02 h⁻¹) compared to higher values at shallower midstream reaches in Pøle (0.23–0.39 h⁻¹) and Havelse streams (0.38–0.98 h⁻¹). This pattern permitted input of CO₂ from soil water to exceed atmospheric loss in the deep, lowermost reaches and, thereby, stream CO₂ concentration to increase (Fig. 4).

A compilation of 539 measurements of CO₂ from six other streams in North Zealand corresponded to those from the Pøle and Havelse streams (median 212 μM, Fig. 5). Groundwater was markedly supersaturated and more than 80% of 133 measurements had CO₂ concentration between 320 and 640 μM (median 460 μM). CO₂ measurements in the outlets from seven eutrophic lakes (n = 1755) ranged from below air saturation during summer to above air saturation in winter and the annual median (29 μM) exceeded air saturation.

Fig. 5

Frequency distribution of daily mean CO₂ concentration (μM) in seven large eutrophic lakes, six streams and four groundwater wells studied throughout the year in North Zealand, Denmark. Medians (m) and number of measurements (n) are shown

CO₂ evasion rate and sources

During summer, CO₂ supersaturation declined tenfold from sunrise to the afternoon at stream stations with intense photosynthesis and CO₂ evasion declined similarly (data not shown). At other stations with reduced photosynthesis, CO₂ concentration and evasion varied much less over the day (i.e. threefold, see Fig. 6). Piston velocity varied much less diurnally than CO₂. Evasion of CO₂ was much larger at high current velocity in the middle of the stream profile than in slower flowing water with low piston velocity close to the banks (Fig. 6).

Fig. 6

Concentration (μM, upper panel), evasion rate (mmol m⁻² h⁻¹, middle panel) and piston velocity for CO₂ (cm h⁻¹, lower panel) during the day at positions close to the shore (filled circles) and at faster flow in the middle of the stream (open circles) at P4 in Pøleå on a day of sustained CO₂ supersaturation. Mean values and SD

Mean daily concentration, evasion and piston velocity of CO₂ changed downstream during June–August (Fig. 7). In the Pøle stream, concentration and evasion of CO₂ (500–1,200 mmol m⁻² day⁻¹) were highest at the two first mid-stream stations (P4 and P5). As a consequence of these high losses, CO₂ depletion and lower evasion rates occurred downstream at the two following stations (P6 and P7). At the stream mouth (P8), CO₂ evasion remained low (100 mmol m⁻² day⁻¹) because of low piston velocity in the deeper, slow-flowing water. In the Havelse stream, CO₂ evasion stayed relatively constant (i.e. 210–265 mmol m⁻² day⁻¹) at mid-stream stations (H5 and H7) located 8 and 17 km from the source, but as in the Pøle stream, evasion tended to be higher upstream (235–470 mmol m⁻² day⁻¹ at H3) and markedly lower (25 mmol m⁻² day⁻¹) in slow-flowing water at the outlet (H8, Fig. 7).

Fig. 7

Mean daily concentration (μM, first panel), piston velocity (cm h⁻¹, second panel) and evasion rate for CO₂ (mmol m⁻² day⁻¹, third panel) at different distances downstream in the Pøle and Havelse streams in June–July (closed circles) and August (open circles). Mean values and SD

The main annual input of CO₂ to the streams (79–94%) was as dissolved free CO₂ in soil water, while CO₂ release from degradation of easily degradable organic matter in the water (BOD) was a minor source (Table 1). Output of CO₂ through evasion to the atmosphere (70–74%) and export via the outlet (26–30%) approximately matched the input.

Table 1 Sources and rates of annual CO₂ import and export for Pøle and Havelse streams

Total annual carbon loss from terrestrial soils to Pøle and Havelse streams was dominated by CO₂ consumed in dissolution of minerals to form HCO₃ ⁻ (1,596 and 1,395 tons C, respectively) and organic carbon export (539 and 281 tons C) compared to export of dissolved CO₂ (172 and 160 tons, Table 1). These annual export rates are substantial when scaled to catchment area of Pøle (25.1 g C m⁻²) and Havelse streams (14.1 g C m⁻²).

Piston velocity and empirical models

Repeated measurements during the day for every location of the flux chamber yielded 55 mean daily values of evasion rate and piston velocity. Piston velocity (K ²⁰_L ) ranged from 0.4 to 21.6 cm h⁻¹ and had an approximately normal distribution with most values (63%) between 4 and 12 cm h⁻¹. Piston velocity increased significantly with current velocity according to a log–log linear least square regression (P < 0.0001, slope 0.742; Table 2). The negative influence of increasing water depth on piston velocity was not significant (P = 0.11).

Table 2 Significant relationships (P < 0.0001) of piston velocity (K_L at 20°C, cm h⁻¹) as a function of current velocity (U, m s⁻¹) and water depth (H, m)

Almost the same relationship of piston velocity to current velocity was found for 200 triplicate measurements (slope 0.776), but the negative relationship to water depth was significant as “n” was greater, although it accounted for only 18% of the variability (Table 2). In multiple regression models, current velocity contributed most and water depth less to the prediction of piston velocity, but the total variability accounted for was almost the same (72%) as that attained by current velocity alone.

Discussion

CO₂ supersaturation in streams

Havelse, Pøle and other streams in North Zealand were greatly supersaturated with CO₂ due to the year-round inflow of CO₂-rich soil water, the short retention time (<24 h) and the surplus of respiration to photosynthesis (Simonsen 1974; Sand-Jensen 1997). Increasing contact time with the atmosphere can account for the decline of CO₂ from upstream to midstream reaches of the Havelse and Pøle streams, while declining evasion rates can account for the increased CO₂ concentration in the slow-flowing lowermost reaches.

The widespread CO₂ supersaturation in lowland streams is a prerequisite for the existence of a diverse community of amphibious plants (Riis et al. 2001) which are unable to use HCO₃ ⁻ and, therefore, require high CO₂ concentration to attain sufficient photosynthesis (Sand-Jensen and Frost-Christensen 1998). The amphibious species are unable to grow in lake outlets because long water retention time and phytoplankton photosynthesis in the lakes often reduce CO₂ to below air saturation during summer resulting in negative net photosynthesis by the amphibious species (Sand-Jensen and Frost-Christensen 1998).

Photosynthesis of aquatic species in the two study streams contributed to the lower CO₂ concentration during summer than winter (Fig. 4) and caused a mean 2.7-fold reduction of CO₂ from sunrise (105–749 μM) to late afternoon (25–479 μM) during 24 diurnal summer measurements. In no instance did the CO₂ concentration fall below air saturation. Thus, CO₂ exchange was consistently directed from the stream waters to the atmosphere in accordance with previous studies in temperate lowland (Rebsdorf et al. 1991; Neal et al. 1998) and upland streams (Hope et al. 2001) and in boreal streams (Sobek et al. 2003).

The contrast between annual median CO₂ concentration in groundwater (460 μM), streams (212 μM) and lake outlets (29 μM) in North Zealand has several important implications. Soil water is the main contribution to the systematic CO₂ supersaturation in the streams and to the substantial CO₂ evasion as confirmed by mass balances (Table 1). CO₂ concentration in the lakes are only slightly above air saturation suggesting that the annual CO₂ flux is usually directed from the lake water to the atmosphere, though at much lower rates than from the streams, due to the 10–20 times lower water–air CO₂ gradient and the lower piston velocity compared to streams. For the largest and most wind-exposed of the seven lakes in North Zealand (Lake Arresø, area = 38 km²), the annual mean piston velocities (K_L) were estimated to 6.9 cm h⁻¹ for 2 years using the model by Jonsson et al. (2008) and continuous wind measurements. For the two streams the mean piston velocity of 8.4 cm h⁻¹ was 1.2 times higher. The larger air–water gradient and piston velocity in the streams imply that the mean CO₂ evasion rates per m² are at least 15-fold higher from streams than large lakes.

Piston velocity

There are several advantages of directly measuring CO₂ evasion rates and concentration differences between water and air and calculating piston velocity from the two parameters instead of relying on indirect methods. First, direct measurements were highly accurate and reproducible. Second, establishment of close relationships between piston velocity and current velocity permitted up-scaling of evasion rates to entire streams and annual rates. Third, several uncertainties associated with indirect methods and conversion from measurements of trace gases to CO₂ were avoided.

Direct measurements of CO₂ evasion rate and CO₂ concentration in air and water were fast, sensitive and highly reproducible. CO₂ concentrations were here derived from determination of alkalinity, pH and temperature in discrete water samples, but continuously operating and reliable pH and temperature sensors are available (e.g. Maberly 1996) and alkalinity can be derived from continuously operating conductivity probes (Sand-Jensen and Frost-Christensen 1998). New techniques are also available to directly measure dissolved CO₂ in freshwaters (Johnson et al. 2010).

There are also potential drawbacks in the use of CO₂ flux chambers, however. First, there are potential errors by the use of flux chambers because water and air turbulence, air temperature and pressure can be influenced by the presence of the chamber (Bilett and Moore 2008). With the chamber construction used here, we could perform the measurement over very short time intervals and avoid changes in air temperature and pressure but we have no measurements of water turbulence to document that it was entirely unaffected by the presence of the chamber, although it was constructed with that purpose. Secondly, it may be difficult to apply flux chambers over very rough water surfaces in stream riffles which may be hot spots for CO₂ evasion. Such stream sections were not present in the channelized North Zealand streams studied here. Third, upscaling of variable evasion rates from the site specific location of flux chambers to entire stream reaches is time-consuming and may introduce error which is difficult to evaluate. Upscaling is avoided by the use of inert trace gases over long reaches.

Piston velocity increased in close correlation with current velocity across the wide range of velocities (0.01–0.82 m s⁻¹) and water depths (0.09–0.90 m) covered by this study. The relationship between piston velocity and current velocity can be used in most local physical settings in lowland streams over the year to predict piston velocity from current velocity and other hydrological features. Once piston velocity is known, evasion rates can be calculated from temperature and CO₂ concentration in air and water. Air measurement of CO₂ concentrations can apparently be left out in most cases because they are either very close to mean atmospheric levels or elevated concentration just above the stream surfaces only occur briefly during very calm nights and mornings when CO₂ concentration in the water is often so high that the outward CO₂ gradient is barely reduced. Water current velocity for prediction of piston velocity is either available from periodic measurements or it can be derived from measurements in a routine hydraulic program. As a result, it becomes realistic to determine annual CO₂ evasion rate for all streams within a catchment.

The relationship of piston velocity to current velocity in the stream may reflect a more direct coupling to surface turbulence (Moog and Jirta 1999) as previously documented for lowland streams (Sand-Jensen and Pedersen 1999). Thus, we cannot dismiss the possibility that a strong empirical relationship between piston velocity and current velocity, as established here for channelized streams, varies appreciably between stream types depending on channel morphology, depth patterns and bed roughness influencing the turbulence regime. If so, more general predictors of piston velocity should be sought and near-surface turbulence appears to be a promising parameter (Zappa et al. 2007) although relationships of piston velocity to turbulent dissipation rate so far have not attained the same predictive power as that of piston velocity to current velocity presented here.

Measurements of evasion rate and piston velocity along reaches have the advantage of covering the relevant scale for budget calculation, but those available have the disadvantage of limited replication and use of gases (e.g., oxygen, propane, ethane, SF₆) which requires conversion to CO₂ (Cole and Caraco 1998). This conversion may induce error when the studied gases behave differently or unexpectedly to that of CO₂ in water, in air and over the interface separating them (Simonsen 1974; Thyssen and Kelly 1985). For example, CO₂ takes part in complex pH-dependent conversions in the stream water, in rainwater and in the dew that forms above streams during nights and early mornings (Ho et al. 1997). The resistance to passage of different gases through organic layers on stream surfaces (Frew 1997) is not predictable from molecular weight if differences in solubility between test gases and CO₂ influence passage across the interface. Consequently, there is room for subjectivity and analytical variability in the use of equations converting the piston velocity of, for example, propane to CO₂ (Genereux and Hemond 1992; Hope et al. 2001). One solution to these shortcomings and an independent check of the data could be to take advantage of the direct approach used here and combine it with full-scale measurements by covering entire reaches with transparent gas-tight material that encloses a large air volume for measurement of CO₂ accumulation rates over time.

CO₂ evasion from streams: a wider perspective

Daily evasion rates during summer were highest (170–1,200 mmol m⁻²) in the middle parts of the Pøle and Havelse streams where CO₂-rich soil water entered shallow reaches with relatively fast flow. Rates were markedly lower (25–100 mmol m⁻² day⁻¹) further downstream in the deeper, slow-flowing reaches because of the lower piston velocity (Table 3). The annual mean CO₂ evasion rate was 395 in the Havelse stream and 495 mmol m⁻² day⁻¹ in the Pøle stream (Table 3). These values are about 5–10 times higher than the average formation of excess CO₂ within systems as a result of greater ecosystem respiration than gross production in the compilation of data from 62 streams (100 mmol m⁻² day⁻¹) and 37 rivers (55 mmol m⁻² day⁻¹; Battin et al. 2008). This comparison supports our conclusion that the main CO₂ source to the evasion from the two lowland streams (79–94%) was dissolved free CO₂ in soil water, while CO₂ release from degradation of imported easily degradable organic matter (BOD) represented a minor source (Table 1). Input of degradable organic matter would make a greater contribution if the streams had been longer and more time had been available for degradation of imported organic material and if untreated sewage and not tertiary treated sewage had been received.

Table 3 Daily mean CO₂ evasion to the atmosphere from selected sub-Arctic and temperate streams and rivers in different settings

The 50-fold range of daily evasion rates at different reaches in the Pøle and Havelse streams (25–1,200 mmol m⁻² day⁻¹) covers most of the global range of mean CO₂ evasion rates for different subarctic streams (10–115 mmol m⁻² day⁻¹, Kling et al. 1991) and temperate streams in either open lowlands (20–3,820 mmol m⁻² day⁻¹, Raymond et al. 1997; Worall and Burt 2005), forest-covered lowlands (Silvennoinen et al. 2008), and in upland peat lands (Hope et al. 2001; Table 3). CO₂ evasion rates are also highly variable from lake surfaces (e.g. 0.1–25 mmol m⁻² day⁻¹, Sand-Jensen and Staehr 2009), but the levels are two orders of magnitude lower per surface area in lakes than streams because of lower concentrations of CO₂ in the surface waters. This contrast between streams and lakes also exists in the catchment areas of the Pøle stream. Thus, the mean evasion rate was 3 mmol m⁻² day⁻¹ from the large Lake Arresø located downstream (Fig. 1) and 14 mmol m⁻² day⁻¹ for 19 small lakes located within the catchment (Sand-Jensen and Staehr 2009). The 19 small lakes had an annual CO₂ evasion of 5 × 10⁶ mol compared with 16 × 10⁶ from the stream. The annual CO₂ evasion was larger from downstream Lake Arresø (42 × 10⁶ mol) in the particular years. In the Havelse catchment lakes were absent and all aquatic CO₂ evasion was from the stream surfaces.

Scaled to surface area of the catchments, daily mean CO₂ evasion rates from freshwaters were 1.9 mmol m⁻² day⁻¹ for the Pøle catchment (including downstream Lake Arresø) and 0.21 mmol m⁻² day⁻¹ for the Havelse catchment. Similar CO₂ evasion rates from surface waters scaled to catchment area were estimated in a Canadian peatland (Bilett and Moore 2008). Total carbon loss from terrestrial soils via the hydraulic cycle in North Zealand are more substantial, however, because, in addition to dissolved CO₂, organic carbon is also exported and CO₂ is consumed in dissolution of minerals to form high HCO₃ ⁻ concentrations in the effluent water. Total carbon losses from terrestrial soils with the water flow amounted to daily means of 5.7 and 3.2 mmol m⁻² day⁻¹ for Pøle and Havelse catchments which are substantial rates in the carbon flux budget of terrestrial habitats amounting to 3–50% of the net production rates of beech forests (typically 11–125 mmol m⁻² day⁻¹, Granier et al. 2000).

In conclusion, our results document the considerable variability of CO₂ evasion rate from upstream to downstream reaches within streams, between different streams and among streams and lakes from the same region. To integrate evasion rates into overall budgets for all water bodies within catchments requires programs for measuring or predicting CO₂ concentration and piston velocity with a high spatial and temporal resolution that has now become practically possible thanks to continuously operating sensors and formulation of general empirical predictions of piston velocity. From the catchment fluxes presented here it is evident that considerable amounts of carbon are lost from terrestrial soils as CO₂, HCO₃ ⁻ and organic carbon via the hydrological cycle and must be included in the carbon budgets of streams, lakes as well as terrestrial ecosystems to attain reliable results.