Outgassing of carbon dioxide (CO2) from rivers and streams to the atmosphere is a major loss term in the coupled terrestrial-aquatic carbon cycle of major low-gradient river systems (the term “river system” encompasses the rivers and streams of all sizes that compose the drainage network in a river basin). However, the magnitude and controls on this important carbon flux are not well quantified. We measured carbon dioxide flux rates (FCO2), gas transfer velocity (k), and partial pressures (pCO2) in rivers and streams of the Amazon and Mekong river systems in South America and Southeast Asia, respectively. FCO2 and k values were significantly higher in small rivers and streams (channels <100 m wide) than in large rivers (channels >100 m wide). Small rivers and streams also had substantially higher variability in k values than large rivers. Observed FCO2 and k values suggest that previous estimates of basinwide CO2 evasion from tropical rivers and wetlands have been conservative and are likely to be revised upward substantially in the future. Data from the present study combined with data compiled from the literature collectively suggest that the physical control of gas exchange velocities and fluxes in low-gradient river systems makes a transition from the dominance of wind control at the largest spatial scales (in estuaries and river mainstems) toward increasing importance of water current velocity and depth at progressively smaller channel dimensions upstream. These results highlight the importance of incorporating scale-appropriate k values into basinwide models of whole ecosystem carbon balance.
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 Quantifying the exchange of biogeochemically active gases such as carbon dioxide (CO2) and oxygen (O2) between atmospheric and aquatic reservoirs plays a critical role in at least three types of studies: (1) the formulation of regional to global carbon budgets, (2) understanding processes related to water quality and pollution, and (3) rate studies of metabolic/ecological processes (i.e., production and respiration). Typically, carbon budget studies involving air-water gas exchange have been carried out in large-scale ecosystems (large rivers, large lakes, and global ocean) [e.g., Richey et al., 2002; Alin and Johnson, 2007; Takahashi et al., 2009], whereas studies addressing water quality or metabolic rates have been done in small lake or stream-scale systems [e.g., Melching and Flores, 1999; Hall and Tank, 2003; Hanson et al., 2006]. As a consequence of the different sizes of the study ecosystems as well as the differing goals of studies across these fields, the literature on gas exchange can be difficult to reconcile across the boundaries of different types of ecosystems (e.g., streams vs. rivers). In this paper, we focus on the role of air-water CO2 exchange in the rivers and streams of major low-gradient river systems in regional to global carbon budgets, with the ultimate goal of improving our ability to scale up small-scale observations to meaningful basin-scale flux estimates. To do so, it is critical to be able to glean insights from the frequently disjunct historical bodies of literature on stream and river-estuary gas exchange.
 The flux of CO2 across the air-water interface (FCO2, mol m−2 s−1) is described by the following equation:
where k is the gas transfer velocity at the in situ temperature (m s−1 or cm h−1), Cw is the CO2 gas concentration in the well-mixed bulk fluid underlying the surface skin (mol m−3), and C0 is the CO2 gas concentration at the water surface in exchange with the atmosphere [Wanninkhof et al., 2009]. Cw and C0 are typically calculated from the CO2 solubility, K0 (mol m−3 atm−1), and the partial pressure of CO2 (pCO2, μatm or 10−6 atm) in the water (pCO2w) and air (pCO2a), respectively (i.e., Cw,0 = K0 × pCO2w,a). Positive values of FCO2 represent fluxes from the water to air, and negative FCO2 values indicate CO2 invasion from air to water. Measuring pCO2 in air and water samples is straightforward [Hesslein et al., 1991], and solubility can be calculated on the basis of temperature [Weiss, 1974]. However, k is difficult to measure accurately.
 The magnitude of k is controlled by microscale turbulence on the water side of the air-water interface [Jähne and Hauβecker, 1998]. Gas exchange fluxes and k may vary widely across environment types as the physical factors controlling them change [cf. Kremer et al., 2003a]. Temperature-normalized gas transfer velocity values (k600) are used in parameterizations relating gas exchange to environmental drivers such as wind speed, where k600 represents the freshwater gas transfer velocity at a temperature of 20°C. In lakes and the open ocean, the dominant controls on surface turbulence, and thus gas transfer, are wind speed and penetrative convection [e.g., Wanninkhof, 1992; Cole and Caraco, 1998; MacIntyre et al., 2002]. In stream environments, k600 has classically been modeled as a function of stream depth, water current velocity, discharge, and slope [e.g., O'Connor and Dobbins, 1958; Owens et al., 1964; Wilcock, 1984; Melching and Flores, 1999]. Studies of gas exchange in estuarine systems indicate that wind speed, water current velocity, and water depth all contribute to the rate of air-water gas transfer [Borges et al., 2004a, 2004b]. Fetch is also important and decreases steeply along a gradient from the open ocean to river headwaters. In large river systems, we expect that a transition occurs in the dominant physical controls on gas exchange as one traverses a landscape from shallow stream channels sheltered from the wind by forest canopies to deep, wide channels where wind impinges on the water surface.
 The turbulence controlling k600 in river systems should thus be induced by a dynamic and channel size-dependent combination of water currents, depth (a proxy for the effects of channel bed friction), and wind (speed and fetch). A large literature exists on gas exchange and reaeration at the stream scale [e.g., Owens et al., 1964; Wanninkhof et al., 1990; Genereux and Hemond, 1992; Melching and Flores, 1999; Hall and Tank, 2003], and several articles have also been published on gas exchange in large rivers [e.g., Elsinger and Moore, 1983; Devol et al., 1987; Clark et al., 1994; Ho et al., 2002]. However, generally the methods for collecting and analyzing data as well as conventions for data reporting are sufficiently divergent between the stream and river gas flux literatures that it is difficult to attribute observed differences in fluxes and transfer velocities across the size spectrum of lotic systems to natural processes when methodological and analytical artifacts may also influence the results. Further, estuarine ecosystems vary in the magnitude of their observed k600 values, depending on exposure to wind (i.e., fetch) and the strength of tidal currents [Kremer et al., 2003a; Borges et al., 2004a], highlighting the importance of taking measurements in a wide range of environments before attempting to delineate a generalized relationship between k600 and physical factors, such as wind speed, water depth, and current velocity. Thus, quantifying CO2 fluxes across an entire river system requires a large number of spatially distributed measurements to parameterize the physical controls on k600.
 This study sought to measure air-water CO2 exchange fluxes and k600 values in low-gradient river systems in a consistent and logistically tractable manner from the widest river channels to the smallest streams. An important application of this work will be to facilitate the accurate upscaling of CO2 evasion across major river systems from headwater streams to estuaries. For example, estimates suggest that lowland tropical rivers outgas 10-fold more carbon as CO2 than is lost to the global oceans as organic matter through river export [Richey et al., 2002]. This global estimate is based on work in the Amazon River basin, where the estimated 0.5 Gt C a−1 lost as CO2 to the atmosphere from Amazonian rivers and wetlands is based on k600 and pCO2 measurements collected only in large-river milieus within the Amazon mainstem corridor, which accounts for less than one third of the total area of the basin [Richey et al., 2002]. To generate more accurate basinwide carbon budgets or estimates of the contribution of rivers to the global carbon cycle, it is essential to better understand what transitions the key physical controls on gas exchange undergo along a size spectrum from first-order streams to the mainstem channels of the largest rivers in the world. To this end, we measured carbon dioxide flux and transfer velocity in rivers and streams across a wide range of channel widths, from a few meters to kilometers, to determine the magnitude of differences in gas exchange fluxes and transfer velocities across this channel-size spectrum and to understand what the corresponding physical controls are. To the extent possible, we use the reporting conventions of the gas exchange literature rather than the reaeration literature because they facilitate more straightforward intercomparability across environment types on the stream-to-ocean continuum.
2. Study Areas
 All field measurements for this study were conducted in the Amazon and Mekong river systems. The Amazon River originates in the Andes Mountains and drains nearly 7 million km2 of South America (Figure 1a). The Amazon River accounts for 20% of global freshwater discharge to the ocean and delivers an average of 3 Mt d−1 of sediment to the ocean [Dunne et al., 1998]. The variety of chemical conditions existing among aquatic environments in the Amazon is impressive, with measured pH values ranging from 3.1 to 8.9; pCO2 values that are usually supersaturated and range from below atmospheric equilibrium to >50-fold higher (∼140 to >20,000 μatm); and wide ranges in dissolved organic carbon concentration (<1–35 mg L−1) and suspended sediment loads (<1–1960 mg L−1) (A. V. Krusche and others, unpublished data, 2010).
 The Mekong River drains ∼800,000 km2 of Southeast Asia, originating in the Himalayas and running through China, Tibet, Burma, Laos, Thailand, and Cambodia before emptying into the South China Sea in Vietnam (Figure 1b). Supersaturated pCO2 conditions are also typical in the Mekong River system, with an observed range from 200 to ∼11,500 μatm, and suspended sediment loads are similarly variable when compared to the Amazon River system (∼2–1044 mg L−1) (J. E. Richey and others, unpublished data, 2010). Within the Mekong River basin, the Tonle Sap system represents an important part of the lowland drainage, including Tonle Sap Great Lake of 2700–16,000 km2 that is connected to the Mekong mainstem by the Tonle Sap River, which reverses flow during the annual hydrological cycle to alternately fill or drain the lake. The human population is denser in the Mekong River basin, with an average of 5–250 people km−2, compared to the Amazon River basin, which averages 1–4 people km−2 throughout most of the basin [Center for International Earth Science Information Network, 2000]. Consequently, land use is generally both more extensive and more intensive in the Mekong River basin.
3.1. Field Work
 We measured carbon dioxide flux and transfer velocity in rivers and streams with channel widths ranging from meters to kilometers. We divided rivers into size categories of greater than and less than 100 m wide (referred to as large and small rivers, respectively) because this threshold has been used in previous basinwide outgassing estimates and is appropriate for differentiating smaller from larger channels in remotely sensed images [Richey et al., 2002; Rasera et al., 2008]. The latter category includes both small rivers and streams and was chosen on the basis of recent work showing that rivers <100 m wide compose >90% of the total length of river networks and may account for >80% of the outgassing flux within individual basins [Mayorga et al., 2005; Rasera et al., 2008]. However, the 100-m threshold is operational rather than physically meaningful. The category of rivers <100 m wide includes streams down to ∼1–2 m across. We note that with respect to gas exchange studies in the literature, there is a gap between those studies conducted on stream-scale channels and those conducted on large-river mainstems.
 Several fieldwork campaigns occurred between June 2004 and January 2007 in the Amazon River basin (Figure 1a and Table 1), with discharge conditions ranging from low to high flow. The sampled areas span the spectrum of chemical characteristics observed across the entire basin, including, for example, both low and high pH values and suspended sediment loads.
Table 1. Chamber Flux Data and Related Measurements
Missing values for water temperature were filled in when possible using data from nearby sampling locations and times. The sensitivity of calculations to water temperature in the range observed through the study area is small.
The k600 data for the pCO2 values in italics were excluded from regression analyses because the calculation error on samples with ΔpCO2 < 200 μatm is high [Borges et al., 2004a].
Data in italics in these columns were excluded from the calculation of average values and all statistical comparisons because the value was identified as an outlier.
Mainstem stations 2–5 were occupied during a transect of the Rio Negro from Manaus to São Gabriel da Cachoeira during March 2005.
 Measurements on the Mekong River occurred during two trips to Southeast Asia in September and October 2004 and September 2005 during conditions of peak discharge. Flux measurements in the Mekong River basin occurred along the mainstem and in tributaries of the Mekong and the Tonle Sap (Figure 1b and Table 1).
3.2. Floating Chamber Method
 To measure CO2 fluxes and transfer velocities, we deployed floating chambers equipped with an internal fan to circulate air through the chamber [see Sebacher et al., 1983]. The chamber (50 cm length × 20 cm width × 20 cm height) was made of Plexiglas with a stopcock in the top to release air pressure. The chamber was connected via CO2-impermeable tubing to a portable infrared CO2 analyzer (LI-820; LI-COR Instruments). Air was circulated through the LI-820 system via an air filter using a miniature air pump (AS-200; Spectrex) with a flow of approximately 150 mL min−1. Closed-cell foam was used for flotation.
 To take chamber measurements, we gently placed the chamber on the water surface to avoid inducing additional turbulence. Data were recorded continuously on a laptop or data logger at 1–5 s intervals from the time the chamber was placed on the water for 5 min or until the CO2 accumulation curve began to flatten out.
 Floating chambers generate results consistent with mass balance and injected tracer methods of measuring gas exchange when the chamber is moving at the same speed as the water surface (rather than being tethered to a stationary object) and at wind speeds less than 8–10 m s−1 and low to moderate wave conditions [Kremer et al., 2003b; Cole et al., 2010]. Chambers with and without fans have been found to give results within the range of normal variability when used under moderately windy conditions (<5 m s−1) [Kremer et al., 2003b]. These conditions were routinely met during our deployments.
 Chamber measurements on rivers with navigable channels were executed from small boats (both river size classes) while drifting with the river current. In streams and the smallest river environments, measurements were conducted from shore, with the chamber deployed in parts of the channel where the chamber was not pulled downstream by the current and was connected to shore by way of the lines connecting it to the gas analyzer. The rope securing the chamber to shore was not taut during any of the measurements reported here. However, these locations may not be representative of the entire cross section of the stream, as water current velocity may be lower and water depth shallower than in the main flow of the stream. These factors would tend to decrease and increase k600, respectively. Thus, these measurements may not be representative of conditions across the entire channel.
3.3. The pCO2 Measurements
 We measured the partial pressure of CO2 at each site by headspace equilibration. A 1 L polycarbonate bottle was overflowed for two to three volume changes, with water pumped from the upper meter of the water column before securely sealing the bottle with a stopper fitted with stopcocks [Hesslein et al., 1991]. A headspace of 60 mL of ambient air (collected from upwind and overhead to avoid elevated CO2 concentrations from breath and motors, for example) was introduced into the bottle while removing the same volume of water. The bottle was shaken vigorously for at least 60 s. The headspace was then removed while the water was reinjected at the same rate. Air samples were also collected in syringes to measure air pCO2.
 All pCO2 samples were measured by infrared gas analysis on a LI-COR LI-820 using standards of approximately 300, 1000, and 10,000 μatm CO2 in nitrogen (Scott Specialty Gases). Samples were run directly from syringes within 24 h of collection or were stored in vials previously flushed with nitrogen until analysis. Vial-stored pCO2 values were corrected for dilution by the nitrogen remaining in the vials after evacuation with a hand pump (15%).
3.4. Chamber Data Analysis
 Air-water gas exchange fluxes were calculated as follows:
where d(pCO2)/dt is the slope of the CO2 accumulation in the chamber (μatm s−1), V is the chamber volume (L), TK is air temperature (in degrees Kelvin, K), S is the surface area of the chamber at the water surface (m2), and R is the gas constant (L atm K−1 mol−1) [Frankignoulle, 1988]. Fluxes were calculated using the first 30, 60, and 90 s of the initial CO2 accumulation in the chamber. The k value measured during each chamber deployment was calculated as follows:
where h is the chamber height (cm), α is the Ostwald solubility coefficient (dimensionless), t is time (s), and the subscripts w, a, i, and f represent water, air, initial, and final, respectively [MacIntyre et al., 1995]. The Ostwald solubility coefficient can be calculated from K0 as a function of temperature as described by Wanninkhof et al. . To compare gas transfer velocity values among sites, k values were normalized to a temperature of 20°C (i.e., k600) using the following equation:
where kT is the measured k value at the in situ temperature (T), ScT is the Schmidt number for temperature T, and the Schmidt number for 20°C in freshwater is 600 [Jähne et al., 1987]. The Schmidt value for freshwater is calculated as a function of temperature:
 In addition to chamber and pCO2 measurements, we measured wind speed and air and water temperatures. Wind speed was measured for 3–5 min at the time of flux measurements using a hand-held anemometer (Kestrel 3000) facing into the wind at ∼1.5 m above the water surface. Wind speeds were averaged over the period of the flux measurement as described by Borges et al. [2004a, 2004b]. Wind speeds were normalized to a height of 10 m above the surface using the following equation:
where ūz is mean wind speed (m s−1) at the height z, u* is friction velocity (m s−1), κ is von Karman's constant (≅0.40), and z0 is roughness length (10−5 m, an intermediate value for water surfaces) [Oke, 1988]. Friction velocity was first calculated by rearranging equation (6) to solve for u* and using the mean wind speed measured at 1.5 m as ūz. Air temperature was also measured with the Kestrel 3000. Water temperature was measured with a Thermo-Orion pH or dissolved oxygen probe.
 For a subset of the Rasera et al.  small-river measurements (n = 14 of 40), water current velocity (w, cm s−1), depth (z, m), and discharge (Q, m3 s−1) were measured using a General Oceanics flow meter (model 2030) at the same time chamber flux measurements were taken. Flow measurements were either taken from bridges or near shore and thus may not represent the current velocity at the exact site of the chamber measurement. Further, as the measurements were taken at only a single point for each site, current velocity data can only be viewed as estimates rather than sitewide averages of water current velocity.
 For all other sampling events, no water current velocity or discharge data were available at the same stations and times that flux measurements were taken. For the purpose of qualitative comparisons of velocity, discharge, and water depth, we obtained data on average discharge, current velocity, and depth at the time of sampling or from long-term monthly or weekly averages from the nearest monitoring station(s). For sites in the Amazon, hydrological data came from the Brazilian national water agency web site (Agência Nacional de Águas, http://hidroweb.ana.gov.br), and for Mekong sites, hydrological data came from Mekong River Commission monitoring stations [cf. Costa-Cabral et al., 2008].
3.6. Data Analysis and Statistics
 Prior to statistical analysis, we divided the results into the two river size class categories for river channels greater than and less than 100 m wide. For the purposes of all statistical analyses, extreme outliers were excluded from the FCO2 and k600 data sets. Extreme outliers were defined as those data beyond the outer fences on boxplots constructed for each size category (http://www.itl.nist.gov/div898/handbook/). In total, one outlier was excluded from the small-river FCO2 data set, and five and two outliers were excluded from the large-river and small-river k600 data sets, respectively. We also excluded k600 data from statistical analysis when the air-water pCO2 gradient (ΔpCO2) was less than 200 μatm, as the error in the k600 calculation increases steeply as ΔpCO2 approaches zero [Borges et al., 2004a]. All outliers and low ΔpCO2 samples that have been excluded from statistical analyses are identified in Table 1.
 Differences between small and large rivers were tested using two-tailed Fisher's t-tests for all parameters. Probability density function (PDF) plots were generated for all flux and gas transfer parameters as well as ancillary environmental variables using the kernel density estimation function in R to compare the distribution of data in the small-river and large-river data sets. PDFs essentially represent smoothed histograms and reflect the relative likelihood that values for each parameter fall into a given range of values.
 Within each river size category, we examined relationships between k600 and estimates of the controlling physical processes and compared our results with previously published estimates. For the subset of small-river chamber flux measurements for which flow data were available, we used stepwise multiple linear regression to evaluate models for the dependence of k600 on physical parameters including wind speed, current velocity, and water depth. For large-river measurements, simple linear regression was used to test for a statistical relationship between k600 and wind speed, but the water current velocity, depth, and discharge data were not collected sufficiently close to the flux measurements to allow a multiple linear regression including both wind speed and water current velocity.
 Overall, we observed higher average FCO2 and k600 values in small-river and stream environments than in rivers with channels wider than 100 m (averages and standard deviations for all parameters are given in Table 1). Small rivers also showed greater variability in k600 than large rivers. Probability density plots for pCO2, flux, k600, and environmental parameters (T, ū10, w, z, and Q) reveal their distributions across large-river and small-river data sets (Figure 2). Distributions for all parameters overlapped at least to some extent between large and small rivers, but pCO2 was the only parameter for which no statistically significant difference existed between the small-river and large-river data sets (Tables 1 and 2).
Table 2. Statistical Comparisons Between Large and Small Rivers
 After excluding invalid values (i.e., ΔpCO2 < 200 μatm), chamber measurements revealed similar ranges and large variation in FCO2 values in both river size classes, ranging from 0.04 to 14.2 μmol m−2 s−1 in large rivers and from 0.7 to 12.4 μmol m−2 s−1 in small rivers (Figure 2 and Table 1). Average fluxes were ∼40% higher from small rivers than from large rivers, as small rivers had more large fluxes and vice versa (Figure 2 and Tables 1 and 2).
 To account for the larger CO2 fluxes observed in small rivers, either CO2 concentrations or k600 must also differ significantly between river size classes. Partial pressures of CO2 varied across two orders of magnitude in rivers of all sizes, with values of 390–12,620 μatm in large rivers and 140–9,230 μatm in small rivers and streams (Figure 2 and Table 1). There was no statistically significant difference in pCO2 values across the river size spectrum (Tables 1 and 2).
 The data presented here suggest, however, that k600 in small rivers and streams (i.e., channels <100 m wide) was higher on average and more variable than in larger rivers (Figures 2–4) [see also Rasera et al., 2008]. k600 ranged over more than an order of magnitude in both size classes, from 1.2 to 44.5 cm h−1 in large rivers and from 1.0 to 71.1 cm h−1 in small rivers (Table 1). The average k600 in small rivers was nearly 60% higher than in large rivers, and this difference was significant (Tables 1 and 2).
 Water temperature measurements are essential for normalizing gas transfer velocities to a common temperature (i.e., k600 values). Temperatures in the streams and rivers in this study occupied a relatively small range (24.5–31.2°C; Table 1). Water temperatures in large rivers occupied a narrower range of water temperatures than observed in small rivers (Figure 2). Although the mean temperature in large rivers was significantly higher statistically, the averages were only 1.5°C apart and their ranges overlapped substantially (Tables 1 and 2). To model fluxes of CO2 in real rivers ultimately, in situ water temperatures must be used to convert k600 values to in situ gas transfer velocities (i.e., k). Since temperatures in our study rivers and streams were consistently higher than the k600 standard temperature (20°C), which would not be the case for temperate and high-latitude streams and rivers, our in situ k values are consistently higher than the k600 values, reflecting enhanced gas transfer at higher water temperatures.
 Environmental variables that may explain some of the variance observed in k600 values included wind speed and the hydrological variables (w, z, Q). Average wind speed measurements extrapolated to 10 m above the water surface (ū10) ranged from 0.0 to 5.2 m s−1 over large rivers compared to 0.0 to 2.2 m s−1 for small rivers (Figure 2 and Table 1). Average wind speed was significantly higher over large rivers than over small ones (Tables 1 and 2). Average values for water current velocity, water depth, and discharge for the closest hydrological monitoring stations to chamber flux measurement sites in the Amazon and Mekong basins or for which water current velocity was measured directly by Rasera et al.  are shown in Table 3. The shapes and peak locations for the water current velocity and depth probability distributions were substantially different for large and small rivers, despite some overlap in ranges (Figure 2). Across the entire data set, large-river and small-river discharge occupied almost completely distinct ranges, with each varying by roughly three orders of magnitude (Figure 2). Large rivers had significantly higher average values for all three hydrological parameters than small rivers (Table 2).
Table 3. Hydrological Measurements From Nearest Monitoring Stations for Large Rivers and From Direct Measurements for Small Rivers and Streams
Flux Measurement Location
Average w (cm s−1)
Average z (m)
Average Q (m3 s−1)
Nearest Hydrological Stations on Large Rivers (≥100 m Wide)
25 Sep 2004
Upstream of Luang Prabang
2 Oct 2004
Mainstem transect stations 2–3 and São Gabriel da Cachoeira
4 Mar 2005
Mainstem transect station 4
7 Mar 2005
Mainstem site upstream of Manaus
13 Jul 2005
15 Jul 2005
Solimões—near Madeira confluence
21 Jul 2005
25 Jul 2005
26 Jul 2005
18 Aug 2005
Upstream of Porto Velho
4 Sep 2005
Mainstem north of Phnom Penh
6 Oct 2005
11 Oct 2005
Mainstem north of Phnom Penh
12 Oct 2005
15 Oct 2005
Small Rivers (<100 m Wide) and Streams
18 Aug 2005
20 Aug 2005
31 Aug 2005
27 Nov 2006
11 Dec 2006
11 Dec 2006
13 Dec 2006
13 Dec 2006
15 Dec 2006
11 Jan 2007
11 Jan 2007
11 Jan 2007
11 Jan 2007
23 Jan 2007
 Relationships between wind speed and k600 in large rivers and between water current velocity and k600 in small rivers and streams suggest that the importance of wind speed diminishes upstream as water current velocity becomes a more important driver of gas exchange. k600 was strongly positively correlated with 10 m wind speed (ū10) in rivers >100 m wide (Figure 3 and Table 4). In small rivers and streams, no relationship was observed between k600 and ū10. Differences between small and large rivers in the means and variance of k600 values relative to ū10 reflect the differences in the physical controls on water turbulence across environment types. Small-river k600 was not significantly related to wind speed, despite an apparent increase in binned k600 data with increasing wind speed (Figure 4 and Table 4). (N.B.: Statistical analysis was performed on individual data points, not on bin-averaged data.) The large variance in the binned data, as indicated by the large error bars, clearly outweighs any explanatory power a relationship between wind speed and small-river gas transfer values would offer. Furthermore, exposure of the water surface to wind (i.e., fetch) also typically declines to zero in small streams, as forest canopies shield streams and small rivers from winds.
Table 4. Statistical Relationships Between k600 and Physical Drivers of Gas Exchange
Relationships highlighted in bold are the best parameterizations for this study.
k600 = 4.46 + 7.11 ū10
k600 = 25.12 + 2.77 ū10
k600 = 13.82 + 0.35 w
k600 = 7.98 + 5.84 ū10 + 0.36 w
 Correlations between k600 and water current velocity were not observed for large rivers because we lacked simultaneous data for k600 and w and demonstrated a positive relationship between k600 and w for small rivers and streams. We expect that a relationship would have been observed between k600 and a water current velocity term (i.e., either w or [w/z]0.5) in large rivers if water current velocity data had been collected at the same time and place as the k measurements. In small rivers and streams, k600 and w were positively and significantly correlated (Figure 3c and Table 4). In this study, a combined velocity-depth term did not provide as much explanatory power as velocity alone, perhaps because there was very little variation in the depths of the small rivers and streams surveyed here, or alternatively because the depth was not always measured at the exact location within the channel where the chamber was deployed.
5.1. Physical Controls on k600 in Low-Gradient River Systems
 The air-water interfaces in both large rivers and estuaries are subject to gas exchange forcing by wind and water currents, with the balance of the two determined by a variety of factors, including fetch, tidal range, slope, and discharge. k600 values observed on rivers >100 m wide in this study fell within the range of values observed by other gas exchange studies conducted on large rivers and estuaries (Table 5). Large-river k600 values measured in this study span the range of earlier gas exchange measurements in the Amazon taken using floating chamber and mass balance methods [Devol et al., 1987], although Devol et al. focused only on the largest tributaries and the Amazon mainstem, representing a subset of the large-river class studied here (Table 5). Among water current velocities reported in Table 5, that reported by Devol et al. is the only one with a higher average current velocity than the water current data from hydrological stations representing the approximate hydrological conditions in the present study (Figure 2 and Table 5).
Table 5. Mean and Standard Deviation (Range) of Published Data on k600 in Large Rivers (>100 m Wide) and Estuaries
 In a similar study of k600 using floating chambers, Borges et al. [2004b] found that 60%–80% of the magnitude of k600 in a European estuary (the Scheldt) could be attributed to wind speed (range of averages during measurement periods, 3.3–8.4 m s−1), with the remaining 20%–40% derived from tidal current velocity (range of averages, 9.6–86.1 cm s−1). In the Amazon and Mekong river basins, water velocity in large tributaries and the mainstem are frequently higher than in many estuaries, in the range of 100–300 cm s−1 [e.g., Devol et al., 1987], and wind speeds are generally lower and fetches more limited than those observed in the Scheldt and other estuaries (Figure 5 and Table 5), suggesting that the relative contribution of water current velocity to k600 values should be higher than those observed by Borges et al. [2004b] in the Scheldt. Indeed, k600 values for this study plot 5–10 cm h−1 higher than the k600–ū10 relationship found by Borges et al. [2004b], suggesting a greater influence of water current velocity in driving gas exchange in these large rivers than in the Scheldt estuary (Figures 3 and 4). Thus, we expect that if we had simultaneous water current velocity data to accompany the k600 measurements, a strong correlation with current velocity (or a combined velocity-depth term) would exist. As support for this interpretation, we note the strong linear correlation between average k600 and water current velocity values among the studies in Table 5 (Figure 6a, excluding one outlier from Devol et al.  chamber data), while only a weak relationship between averages for wind speed and k600 was apparent (Figure 6b).
 The higher and highly variable k600 values observed in small rivers and streams were not unexpected. A sensitivity analysis showed that a k600 dependent on (w/z)0.5 was particularly sensitive to changes in water depth at depths shallower than 3 m (not shown), so the variation in water depth and current velocity in small river and stream channels should result in both high variability and high values of k600. For instance, extremely high CO2 outgassing rates observed in first-order Amazonian streams fed by groundwater springs were driven by bed friction as well as by extremely high pCO2 values [Johnson et al., 2008]. Using floating chambers to measure k600 in streams and small rivers requires careful measurement of water depth and current velocity across the channel, such that fluxes measured in areas with lower flow can be extrapolated to reflect conditions in the main flow of the channel. Alternatively, when the channel is big enough to take boat-based measurements, current velocity measurements relevant to chamber fluxes can be approximated by recording GPS boat velocities. To further refine the relationship between k600 and current velocity and to explore the role of water depth (and bed friction) in small rivers, measurements taken over a broader depth range are needed.
 The small-river measurements in this study compare well with a compilation of stream and small-river data from the literature, despite the fact that the small rivers and streams included in this study encompassed a wider range of channel depth, current velocity, and discharge values than in most other studies encountered as well as a narrower range in slope (Table 6). A weak linear relationship exists between k600 values and (w/z)0.5 (Figure 6c). However, many stream studies report gas exchange results as “reaeration coefficients” (K2(20°C) for O2, units of d−1) instead of k600 values and do not report average depths, so that K2 cannot be converted to k600 [e.g., Genereux and Hemond, 1992; Marzolf et al., 1994]. To compare our results more broadly to stream gas transfer studies, we converted the small-river data for which we had depth measurements to reaeration coefficients for CO2 by dividing the k600 values by the water depth (Table 6). Reaeration coefficients reported in the literature for oxygen (K2(O2)) were converted to their CO2 equivalents (K2(CO2)) using equation (4). In terms of reaeration coefficients, the Amazon and Mekong small rivers and streams had some of the lowest K2(CO2) values among those surveyed, which reflects the greater average channel depths in this study than in most other stream gas exchange studies. Average K2(CO2) values and average stream channel depths (z) were strongly correlated (Figure 6d), as would be expected because depth is one of the values used to calculate it, but no significant relationship between current velocities and K2(CO2) was observed.
Table 6. Mean and Standard Deviation (Range) of Published Data on k600 in Small Rivers (<100 m Wide) and Streams
Reaeration Coefficient for CO2, K2(20°C) (h−1)
k600 (cm h−1)
Q (L s−1)
ū10 (m s−1)
w (cm s−1)
The disturbed equilibrium method involves deoxygenating a parcel of water by the addition of sodium sulfate and a cobalt catalyst and measuring the rate of change of oxygen content in that parcel of water as it moves downstream and is reaerated.
5.2. Toward a General Model of Gas Exchange in Low-Gradient River Systems
 A survey of published gas exchange studies in rivers and estuaries indicates that average wind speeds recorded during gas exchange studies are lower over rivers than over estuaries (Figure 5 and Table 5). The converse is true for water current velocities, with higher values in river environments than in estuary environments. The net result of the combined influence of wind and water velocities on gas transfer appears to be higher average k600 values in rivers than in estuaries (grand k600 means of 12.8 ± 10.7 vs. 9.5 ± 5.5 cm h−1, respectively, or 7.2 ± 1.8 cm h−1 for estuaries if the macrotidal Scheldt is excluded).
 Average winds appear to be lowest in small river and stream settings, although these values are not usually reported in stream-scale studies (likely because wind speed is assumed to be less important than stream geomorphology and current velocity) (Figure 4 and Table 6). Water current velocities in small rivers and streams in this study were on average similar to those in estuaries (Figure 4), but in truly stream-scale studies, the average current velocities are about half again lower than in our small-river category, indirectly illustrating the importance of water depth in smaller channels (Table 6, excluding values from this study and Waipa, which have average discharge values more than an order of magnitude higher than the next largest stream study). The lower velocities in classic streams such as Walker Branch likely reflect greater channel roughness than in the low-gradient streams in this study. Average k600 values in the literature survey were 75% (22.4 ± 14.3 cm h−1) and 93% (24.6 ± 14.9 cm h−1) higher in the groups (small rivers and streams) and streams only, respectively, than in large rivers (Table 5 vs. Table 6).
 Collectively, the data presented in this study and those gathered from a broader sampling of the stream, river, and estuary gas exchange literature suggest that gas exchange in the most upstream portions of river systems is dominated by factors related to water current and channel bed friction as sources of turbulence (Figure 7). Moving downriver, wind speed becomes more important as channels widen and protection by forest canopy and/or topography diminishes, but factors related to river flow likely still dominate in terms of generating turbulence at the water surface. In contrast, estuarine systems, where water flow varies with tidal cycles and wind fetches are greater, wind-controlled gas exchange is likely the norm. Even in the macrotidal Scheldt estuary, Borges et al. [2004b] found that only 20%–40% of the magnitude of k600 could be attributed to the action of water currents. Gas exchange in the open ocean, at the far end of the stream-to-ocean transect, is dominated by wind forcing of gas transfer [Wanninkhof et al., 2009]. Thus, within river systems, transitions in the physical controls on k600 occur with the decreasing size of the river channel upstream. As one travels upriver from the estuary to streams of the lowest order, the relative importance of wind in controlling k600 declines to zero while the influence of water current and bed friction progressively increase (Figure 7). Regional models of fluvial biogeochemistry in low-gradient systems must thus be correctly parameterized to reflect this transition to correctly handle upscaling of individual measurements to large-scale carbon budgets appropriately.
5.3. Implications for Regional Carbon Budgets
 The results of this study have implications for modeling gas exchange fluxes at the scale of the whole river basin. The magnitude of CO2 fluxes and physical controls on k600 appear to vary substantially across the river channel-size spectrum (Tables 2, 5, and 6). The Richey et al.  basinwide estimate of CO2 outgassing for the Amazon River system used static values for k in different environments (i.e., not including the effects of wind or current velocity): 9.6 ± 3.8 cm h−1 in the mainstem Amazon River and 5.0 ± 2.1 cm h−1 in both primary tributaries (>100 m wide) and small rivers and streams (<100 m wide). The average k600 value in this study for all rivers >100 m wide, including both mainstem and tributary environments, was 8.0 ± 4.8 cm h−1 for wind speeds under 1 m s−1. When this k600 value is corrected to water temperatures typical of Amazonian aquatic ecosystems (∼25°C–30°C), the average rises to 9.0–10.3 cm h−1, which is comparable to the mainstem k value used by Richey et al.  but roughly twice as large as the value they used for primary tributaries (i.e., tributaries >100 m wide). Richey et al.  did not differentiate between mainstem and primary tributary environments in calculating FCO2 values, but our results suggest that the contribution of primary tributaries to basin-scale CO2 outgassing may be nearly double the Richey et al.  estimate for primary tributaries under a new detailed analysis.
 When the average small river and stream k600 value of 23.3 cm h−1 is corrected to typical tropical river water temperatures, it rises to 26–30 cm h−1, which is five to six times higher than the value used by Richey et al. . All else being equal, the results presented here suggest that the areal CO2 flux rate from rivers <100 m wide may be expected to increase several-fold relative to earlier estimates with the incorporation of a more realistic k600 parameterization for small rivers and streams, particularly if the finding that smaller river channels contribute the majority of the net river system outgassing holds up at the largest scales (e.g., 80%–90% for the Ji-Paraná basin in the work of Rasera et al. ). However, to rigorously revise earlier estimates, it will be necessary to embed the appropriate gas transfer parameterizations into a model containing river channel dimensions and water current velocity information. The tremendous variability seen in the small-river data set highlights the importance of collecting sufficient spatially distributed measurements of gas exchange and related physical variables to ensure that the resulting parameterizations represent the entire drainage network.
 Taken together, recent developments in the analysis of air-water gas exchange in low-gradient river systems will improve our ability to incorporate realistic scale-dependent process information into regional carbon budgets. These advances are expected to increase basinwide CO2 outgassing estimates substantially for inundated areas of the humid tropics. For instance, improvements to a geographic information system-based method for quantifying water surface area and direct flux measurements in rivers <100 m wide suggested that the extent of inundated areas for these rivers has been underestimated by ∼10%, which would increase basinwide CO2 outgassing by a similar proportion [Rasera et al., 2008]. In addition, recent estimates of CO2 losses at the headwater scale suggest that basinwide CO2 outgassing estimates in the Amazon may be augmented by ∼20% through losses from first-order streams, which are not resolvable through remotely sensed images [Johnson et al., 2008]. The present study suggests that CO2 outgassing from small rivers in tropical, low-gradient river systems could be as much as several times higher than previous estimates suggested on the basis of the underestimated k600 used for rivers <100 m wide by Richey et al. . Given that tributaries >100 m wide account for ∼50%–75% of basinwide flux throughout the annual cycle [Richey et al., 2002, Figure 4], a doubling of primary tributary k values alone could increase the basinwide CO2 evasion estimate by ∼50%–75%. However, a new detailed analysis would be necessary to incorporate all of these revisions carefully, along with new data, before estimating an overall change in basin gas evasion estimates. Correctly parameterizing gas exchange processes across the broad range of environment types in river systems is clearly critical to attaining accurate estimates of regional carbon balance. A more realistic model of river k600 driven by wind speed, water current velocity, and depth will allow investigators to refine estimates of basinwide CO2 flux in the Amazon and other major low-gradient river basins using existing hydrological and climatological time series data. Incorporation of wind speed and current velocity data is expected to revise previous estimates of regional river system outgassing substantially upward.
 Physical controls on gas exchange vary substantially along an ocean-to-headwater transect, with a greater importance for wind speed in estuaries and the widest river channels and with progressively increasing importance for water current velocity and water depth at decreasing river channel size. Correct parameterization of gas exchange in regional carbon budgets has important implications for the accurate upscaling of major carbon fluxes. For instance, at low wind speeds and in the Amazon mainstem, k600 values used by Richey et al.  were appropriate and would not lead to regional underestimates or overestimates of CO2 flux. However, the present study highlights the tremendous variability in k600 in smaller rivers and suggests that previous estimates of CO2 outgassing from primary tributaries, small rivers, and streams of the Amazon and other major low-gradient river systems may increase substantially with the incorporation of more appropriate k600 parameterizations. Statistical relationships between gas exchange and physical factors in this study (Table 4) support the model of decreased importance for wind speed in lower-order rivers within large river systems and the greater importance of water current velocity in smaller rivers. However, because of the caveats associated with measurements associated with both large and small rivers in this study, further work is needed to refine appropriate relationships for models that will employ such parameterizations to update regional carbon budgets.
 We thank the many members of the Rede Beija Rio and Naganet field sampling teams in Brazil and Southeast Asia, respectively, for facilitating these field measurements. In particular, we thank Reynaldo Victoria, Suppakorn Chinvanno, Pranisa Wangrungkit, Mao Hak, Nhim Sophea, Mickey Sampson, and Phousy Inthapanya for invaluable logistical support; Erin Ellis, Nei Leite, Vania Neu, Eliete Sousa, Nhim Sophea, Khoum Vanny, Cheak Meng, Phousy Inthapanya, Khammone Xomvimane, and Thongsy Bounpaseut for able assistance in the field; Anthony Aufdenkampe, Patrick Crill, and Vicky Ballester for formative discussions; and Lauren McGeoch for making the maps. Erin Ellis, Sonya Remington, Rob Striegl, and several anonymous reviewers provided feedback on earlier versions of the manuscript that substantially improved this article. We are grateful for funding from the NASA LBA program (NCC5-689 and NNG06GE98A) for research in the Amazon and NSF (EAR-0223521) for research on the Mekong in the United States and from FAPESP (03/07778-5 and 03/13172-2) in Brazil. This is CAMREX contribution 151 and PMEL contribution 3543.