The sampled Lena River main stem and 20 tributaries are located along a 2600 km latitudinal transect SW to NE and include watersheds of distinct sizes, geomorphology, permafrost extent, lithology, climate, and vegetation (Fig. 1, S1A in the Supplement; Table S1 in the Supplement). The total watershed area of the rivers sampled in this work is approximately 1.66 million square kilometers, representing 66 % of the entire Lena River basin. Permafrost is mostly continuous except some discontinuous and sporadic patches in the southern part of the Lena basin (Brown et al., 2002). The mean annual air temperatures (MAATs) along the transect range from -5 ∘C in the southern part of the Lena basin to -9 ∘C in the central part of the basin. The range of MAAT for 20 tributaries is from -4.7 to -15.9 ∘C. The mean annual precipitation ranges from 350–500 mmyr-1 in the southern and southwestern parts of the basin to 200–250 mmyr-1 in the central and northern parts (Chevychelov and Bosikov, 2010). The lithology of the Siberian platform which is drained by the Lena River is highly diverse and includes Archean and Proterozoic crystalline and metamorphic rocks; Upper Proterozoic, Cambrian, and Ordovician dolostones and limestones; volcanic rocks of the Permo–Triassic age; and essentially terrigenous silicate sedimentary rocks of the Phanerozoic. Further description of the Lena River basin landscapes, vegetation, and lithology can be found elsewhere (Rachold et al., 1996; Huh et al., 1998a, b; Pipko et al., 2010; Semiletov et al., 2011; Kutscher et al., 2017; Juhls et al., 2020).

The peak of annual discharge depends on the latitude (Fig. 1) and occurs in May in the south (Ust-Kut) and in June in the middle and low reaches of the Lena River (Yakutsk, Kysyr). From 29 May to 17 June 2016, we moved downstream on the Lena River by boat with an average speed of 30 kmh-1 (Gureyev, 2016). As such, we followed the progression of the spring and moved from the southwest to the northeast, thus collecting river water at approximately the same stage of maximal discharge. Note that transect sampling is a common way to assess river water chemistry in extreme environments (Huh and Edmond, 1999; Spence and Telmer, 2005), and generally, a single sampling during high-flow season provides the best agreement with time-series estimates (Qin et al., 2006). Regular stops each 80–100 km along the Lena River allowed sampling for major hydrochemical parameters and CH4 along the main stem. We also moved 500–1500 m upstream of selected tributaries to record CO2 concentrations for at least 1 h and to sample for river hydrochemistry; see examples of spatial coverage in Fig. S1B. From late afternoon–evening to the next morning, we stopped for sleep but continued to record pCO2 in the Lena River main stem (15 sites, evenly distributed over the full 2600 km transect) and two tributaries (Aldan and Tuolba).

Surface water CO2 concentration was measured continuously, in situ by deploying a portable infrared gas analyzer (IRGA, GMT222 CARBOCAP® probe, Vaisala®; accuracy ±1.5 %) of two ranges (2000 and 10 000 ppm). This system was mounted on a small boat in a perforated steel pipe ∼0.5 m below water surface. The tube had two necessary openings of different diameters, which allowed free water flow with a constant rate while the boat was moving. The probe was enclosed within a waterproof and gas-permeable membrane. The key to aqueous deployment of the IRGA sensor is the use of a protective expanded polytetrafluoroethylene (PTFE) tube or sleeve that is highly permeable to CO2 but impermeable to water (Johnson et al., 2009). The material is available for purchase as a flexible tube that fits over the IRGA sensor (Product number 200-07; International Polymer Engineering, Tempe, Arizona, USA). We also used a copper mesh screen to minimize biofouling effects (i.e., Yoon et al., 2016). However these effects are expected to be low in cold waters of the virtually pristine Lena River and its tributaries. During sampling, the sensor was left to equilibrate in the water for 10 min before measurements were recorded.

The probe was enclosed and placed into a tube which was submerged 0.5 m below the water surface. Within this tube, we designed a special chamber that allowed low-turbulent water flow around the probe without gas bubbles. Previous studies (Park et al., 2021; Crawford et al., 2015; Yoon et al., 2016) reported some effects of boat speed on sensor CO2 measurements due to turbulence. Although the turbulence was minimized in the tube–chamber design used in the present study, on a selected river transect (∼10 km) we have also tested the impact of the boat speed (5, 10, 20, 30, and 40 kmh-1) on the sensor performance and have not detected any sizable (>10 %, p<0.05, n=25) difference in the CO2 concentrations recorded by our system.

A Campbell logger was connected to the system, allowing continuous recording of the CO2 concentration (ppm), water temperature (∘C) and pressure (mbar) every minute during 5 over 10 min intervals yielding 4285 individual pCO2, water temperature, and pressure measurements in total. These data were averaged for three consecutive slots of 5 min measurements, which represented the approximate 20 km interval of the main stem route. CO2 concentrations in the Lena River tributaries were measured over the first 500–2000 m distance upstream of the tributary mouth and comprised between 5 and 34 measurements for daytime visits and between 305 and 323 individual pCO2 readings for each tributary for daytime and nighttime monitoring.

Sensor preparation was conducted in the lab following the method described by Johnson et al. (2009). The measurement unit (MI70, Vaisala®; accuracy ±0.2 %) was connected to the sensor, allowing instantaneous readings of pCO2. The sensors were calibrated in the lab against standard gas mixtures (0, 800, 3000, 8000 ppm; linear regression with R2>0.99) before and after the field campaign. The sensors' drift was 0.03 %–0.06 % per day, and overall error was 4 %–8 % (relative standard deviation, RSD). Following calibration, post-measurement correction of the sensor output induced by changes in water temperature and barometric pressure was done by applying empirically derived coefficients following Johnson et al. (2009). These corrections never exceeded 5 % of the measured values. Furthermore, we tested two different sensors in several sites of the river transect: a main probe used for continuous measurements and another probe used as a control and never employed for continuous measurements. We did not find any sizable (>10 %) difference in measured CO2 concentration between these two probes.

For CH4 analyses, unfiltered water was sampled in 60 mL serum bottles and closed without air bubbles using vinyl stoppers and aluminum caps and immediately poisoned by adding 0.2 mL of saturated HgCl2 via a two-way needle system. In the laboratory, a headspace was created by displacing approx. 40 % of water with N2 (99.999 %). Two 0.5 mL replicates of the equilibrated headspace were analyzed for their concentrations of CH4, using a Bruker GC-456 gas chromatograph (GC) equipped with flame ionization and thermal conductivity detectors. After every 10 samples, a calibration of the detectors was performed using Air Liquid gas standards (i.e., 145 ppmv). Duplicate injection of the samples showed that results were reproducible within ±5 %. The specific gas solubility for CH4 (Yamamoto et al., 1976) was used in calculation of total CH4 content in the vials and then recalculated to µmolL-1 of the initial waters.

The dissolved oxygen (CellOx 325; accuracy of ±5 %), specific conductivity (TetraCon 325; ±1.5 %), and water temperature (±0.2 ∘C) were measured in situ at 20 cm depth using a WTW 3320 multimeter. The pH was measured using a portable Hanna instrument via a combined Schott glass electrode calibrated with NIST buffer solutions (4.01, 6.86, and 9.18 at 25 ∘C), with an uncertainty of 0.01 pH units. The temperature of buffer solutions was within ±5 ∘C of that of the river water. The water was sampled in a pre-cleaned polypropylene bottle from 20–30 cm depth in the middle of the river and immediately filtered through disposable single-use sterile Sartorius filter units (0.45 µm pore size). The first 50 mL of filtrate was discarded. The DOC and dissolved inorganic carbon (DIC) were determined by a Shimadzu TOC-VSCN analyzer (Kyoto, Japan) with an uncertainty of 3 % and a detection limit of 0.1 mgL-1. Blanks of Milli-Q water passed through the filters demonstrated negligible release of DOC from the filter material.

CO2 flux (FCO2) was calculated following Cai and Wang (1998): 1FCO2=KhkCO2Cwater-Cair, where Kh is Henry's constant corrected for temperature and pressure (molL-1atm-1), kCO2 is the gas exchange velocity at a given temperature, Cwater is the water CO2 concentration, and Cair is the CO2 concentration in the ambient air. In order to convert CO2 concentration in water and air into CO2 partial pressure, we followed Wanninkhof et al. (1992) and Lauerwald et al. (2015). We used the average CO2 concentrations of 402 ppm in May–June 2016 (from 129 stations all over the world, https://community.wmo.int/wmo-greenhouse-gas-bulletins, last access: 3 September 2021), which is consistent with the value recorded at the nearest Tiksi station in 2016 (404±0.9 ppm; Ivakhov et al., 2019). Temperature-specific solubility coefficients were used to calculate respective CO2 concentrations in the water following Wanninkhof et al. (1992). To standardize kCO2 to a Schmidt number of 600, we used the following equation (Alin et al., 2011; Vachon et al., 2010): 2k600=kCO2600ScCO2-n, where ScCO2 is CO2 Schmidt number for a given temperature (t, ∘C) in the freshwater (Wanninkhof, 1992): 3ScCO2=1911.1-118.11t+3.4527t2-0.041320t3. The exponent n (Eq. 2) is a coefficient that describes water surface (2/3 for a smooth water surface regime and 1/2 for a rippled and a turbulent one), and the Schmidt number for 20 ∘C in freshwater is 600. We used n=2/3 because all water surfaces of sampled rivers were considered flat and had a laminar flow (Alin et al., 2011; Jähne et al., 1987) with wind speed always below 3.7 ms-1 (Guérin et al., 2007).

In this study, we used a kCO2 (a median gas transfer coefficient) value of 4.464 md-1 measured in the four largest rivers of the Western Siberia Lowland (WSL) in June 2015 (Ob', Pur, Pyakupur, and Taz rivers; Karlsson et al., 2021). These rivers are similar to Lena and its tributaries in size but exhibit lower velocity than those of the Lena River. In fact, due to more mountainous relief, the Lena River main stem and tributaries present much higher turbulence than that of the Ob River and tributaries, and as such the value kCO2 used in this study can be considered rather conservative. This value is consistent with the kCO2 reported for the Kolyma River and its large tributaries (3.9±2.5 md-1; Denfeld et al., 2013), tributaries and main stem of the Yukon River basin (4.9–7.6 md-1; Striegl et al., 2012), large rivers in the Amazon and Mekong basins (3.5±2.1 md-1; Alin et al., 2011) and with modeling results of k for large rivers across the world (3–4 md-1; Raymond et al., 2013). Note that decreasing the k to the most conservative value of 3 md-1 of Raymond et al. (2013) will decrease specific emissions by ca. 30 %.

Instantaneous diffusive CH4 fluxes were calculated using an equation similar to Eq. (1) with k from western Siberia rivers (Serikova et al., 2018), concentrations of dissolved CH4 in the water, and an air–water equilibrium pCH4 concentration of 1.8 ppm, and mean annual pCH4 concentration in the air for 2016 (Mauna Loa Observatory ftp://aftp.cmdl.noaa.gov/products/trends/ch4/ch4_annmean_gl.txt) following standard procedures (Serikova et al., 2018, 2019).

The physio-geographical characteristics of the 20 Lena tributaries sampled in this study and the two points of the Lena main stem (upstream and downstream of the Aldan, Table S1) were determined by applying available digital elevation model (DEM GMTED2010), soil, vegetation, lithological, and geocryological maps. The landscape parameters were typified using the TerraNorte Database of Land Cover of Russia (Bartalev et al., 2011). This included various types of forest (evergreen, deciduous, needleleaf/broadleaf), grassland, tundra, wetlands, water bodies, and other areas. The climate and permafrost parameters of the watershed were obtained from CRU grid data (1950–2016) (Harris et al., 2014) and NCSCD data (10.5879/ecds/00000001, Hugelius et al., 2013), respectively, whereas the biomass and soil OC content was obtained from the BIOMASAR2 (Santoro et al., 2010) and NCSCD databases. The lithology layer was taken from the GIS version of the geological map of the Russian Federation (scale 1:5000000, http://www.geolkarta.ru/, last access: 3 September 2021). To test the effect of carbonate rocks on dissolved C parameters, we distinguished acidic crystalline, terrigenous silicate rocks and dolostones, and limestones of upper Proterozoic, Cambrian, and Ordovician age. We quantified river water surface area using the global SDG database with 30 m2 resolution (Pekel et al., 2016) including both seasonal and permanent water for the open water period of 2016 and for the multiannual average (reference period 2000–2004). We also used a more recent GRWL Mask Database which incorporates first-order wetted streams (Allen and Pavelsky, 2018).

The Pearson rank order correlation coefficient (Rs, p<0.05) was used to determine the relationship between CO2 concentrations and climatic and landscape parameters of the Lena River tributaries. Further statistical treatment of CO2, DIC, and DOC concentration drivers in river waters included a principal component analysis, which allowed us to test the effect of various hydrochemical and climatic parameters on the dissolved C pattern. For the principal component analysis (PCA) treatment, all variables were normalized as necessary in the standard package of STATISTICA-7 (http://www.statsoft.com, last access: 3 September 2021) because the units of measurement for various components were different. The factors were identified via the raw data method. To run the scree test, we plotted the eigenvalues in descending order of their magnitude against their factor numbers. There was significant decrease in the PCA values between F1 and F2, suggesting that a maximum of two factors were interpretable.

The main hydrological C parameters of the Lena River and its tributaries (pCO2, CH4, pH, DIC, and DOC) are listed in Tables 1 and 2. Continuous pCO2 measurements in the main stem (4285 individual data points) averaged for each 20 km interval over the full distance of the boat route demonstrated a sizable increase (from ca. 380 to 1040 µatm) in pCO2 northward (Fig. 2). There was a positive correlation between the pCO2 and distance from the headwaters of the Lena River (r=0.625, p<0.01, Fig. 3a). The CH4 concentration was low (0.054±0.023 and 0.061±0.028 µmolL-1 in the Lena River and 20 tributaries, respectively) and did not change appreciably along the main stem and among the 20 tributaries (Fig. 3b). The DOC concentration did not demonstrate any systematic variations over the main stem (10.5±2.4 mgL-1, Fig. 3c); however it was higher and more variable in tributaries (15.8±8.6 mgL-1). The DIC concentration decreased about 5-fold from the headwaters to the middle course of the Lena River (Fig. 3d), and pH decreased by 0.8 units downstream (Fig. 3e).

Generally, the concentrations of DOC measured in the present study during the peak of the spring flood are at the highest range of previous assessments during summer baseflow (around 5 mgL-1; range of 2 to 12 mgL-1; Cauwet and Sidorov, 1996; Lara et al., 1998; Lobbes et al., 2000; Kuzmin et al., 2009; Kutscher et al., 2017). The DIC concentration in the main stem during spring flood was generally lower than that reported during summer baseflow (around 10 mgL-1; range of 5 to 50 mgL-1) but consistent with values reported in Yakutsk during May and June period (7 to 20 mgL-1, Sun et al., 2018). A sizable decrease in DIC concentration between the headwaters (first 500 km of the river) and the Lena River middle course was also consistent with the alkalinity pattern reported in previous works during summer baseflow (Pipko et al., 2010; Semiletov et al., 2011). For the Lena River tributaries, the most comprehensive data set on major ions was acquired in July–August of 1991–1996 by Huh and Edmond's group (Huh and Edmond, 1999; Huh et al., 1998a, b) and by Sun et al. (2018) in July 2012 and at the end of June 2013. For most tributaries, the concentration of DIC was a factor of 2 to 5 lower during the spring flood compared to summer baseflow. This result can be explained by the strong dilution of carbonate-rich groundwaters feeding the river in spring high flow compared to summer low flow.

The measured pCO2 in the river water and published (Karlsson et al., 2021) gas transfer coefficient (4.46 md-1) allowed for calculation of the CO2 fluxes over the full length of the studied main stem (2600 km) and the sampled tributaries. Calculated CO2 fluxes of the main stem and tributaries ranged from zero and slightly negative (uptake) values in the most southern part of the Lena River and certain tributaries (northern Katyma) to between 0.5–2.0 gCm-2d-1 in the rest of the main stem and tributaries (Tables 1 and 2; Fig. 2b). The largest part of the Lena River main stem, 1429 km from Kirenga to Tuolba, exhibited a quite stable flux of 1.1±0.2 gCm-2d-1. In the last ∼400 km part of the Lena River main stem studied in this work, from Tuolba to Aldan, the calculated fluxes increased to 1.7±0.08 gCm-2d-1.

The river water concentrations of dissolved CH4 in the tributaries and the main channel (0.059±0.006; interquartile (IQR) range from 0.025 to 0.199 µmolL-1; Tables 1 and 2) did not exhibit any trend with distance from headwaters or landscape parameters of the catchments. These values are consistent with the range of CH4 concentration in the low reaches of the Lena River main channel (0.03–0.085 µmolL-1; Bussman, 2013) and are 100–500 times lower than those of CO2. Consequently, diffuse CH4 emissions constituted less than 1 % of total C emissions and are not discussed in further detail.

The continuous diel CO2 measurements of three tributaries (Kirenga, Tuolba, and Aldan) and 14 sites of the Lena River main channel showed generally modest variation with diurnal range within 10 % of the average pCO2 (Figs. 4 and S2 in the Supplement). The observed variations in pCO2 between day and night were not linked to water temperature (p>0.05), which did not vary more than 1–2 ∘C between the day and night periods.

The spatial variations in hydrochemical parameters were tested in the upper reaches of the Lena main stem and its largest tributary – the Aldan River (Fig. S3 in the Supplement). In the Lena River, over a lateral distance of 550 m across the riverbed, the pCO2 and CH4 concentrations were equal to 569±4.6 µatm and 0.0406±0.0074 µmolL-1, respectively, whereas the DIC and DOC concentrations varied <15 % (n=5). In the Aldan River, over a 2700 m transect across the flow, the pCO2 and CH4 concentrations were equal to 1035±95 µatm and 0.078±0.00894 µmolL-1, respectively, whereas DIC and DOC varied within <20 % (n=4). Overall, these results supported our design of punctual (snap shot) sampling in the middle of the river.

The CO2 concentration in the Lena River main stem and tributaries increased from the southwest to northeast (Tables 1 and 2; Fig. 2), and this was reflected in a positive (R=0.66) correlation between CO2 concentration and continuous permafrost coverage and a negative (R=-0.76) correlation with MAAT (Table 3). Among different landscape factors, C stock in the upper 0–30 and 0–100 cm of soil, proportion of riparian vegetation and bare rocks, coverage by deciduous needleleaf forest, and coverage of river watershed by water bodies (mostly lakes) exhibited significant (p<0.01, n=19) positive correlations (0.54≤R≤0.86) with average pCO2 of the Lena River tributaries (Fig. 5). The other potentially important landscape factors of the river watershed (proportion of peatland and bogs, tundra coverage, total aboveground vegetation, type of permafrost, annual precipitation) did not significantly impact the CO2 concentration in the Lena River tributaries (Table 3).

Further assessment of landscape factor control on C parameters of the river water was performed via a PCA. This analysis basically confirmed the results of linear regressions and revealed two factors capable of explaining only 12.5 % and 3.5 % of variability (Fig. S4 in the Supplement). The F1 strongly acted on the sample location at the Lena transect, the content of OC in soils, the watershed coverage by deciduous needleleaf forest and shrubs, riparian vegetation (a proxy for the width of the riparian zone) and proportion of tundra, bare rock and soils, water bodies, peatland, and bogs (>0.90 loading). The pCO2 was significantly linked to F1 (0.72 loading).

The areal emission of CO2 from the lotic waters of the Lena River watershed were assessed based on total river water coverage of the Lena basin in 2016 (28 197 km2, of which 5022 km2 is seasonal water, according to the global SDG database). This value is consistent with the total river surface area from the GRWL Mask database (22 479 km2). Given that the measurements were performed at the peak of the spring flood in 2016, we used the maximal water coverage of the Lena River basin.

Based on past calculated pCO2 of the Lena River (400–1000 µatm; Semiletov, 1999; Semiletov et al., 2011; Pipko et al., 2010), both the seasonality and spatial differences downstream are relatively small. Indeed, for the lower reaches of the Lena River, from Yakutsk to the Lena Delta, Semiletov (1999) and Semiletov et al. (2011) reported, for August–September 1995, an average pCO2 of 538±96 µatm (range 380–727 µatm). This value is very similar to the one obtained in July 2003 for the low reaches of the Lena (559 µatm, Pipko et al., 2010). Over the full length of the Lena River, from Ust-Kut to the Lena mouth, Pipko et al. (2010) reported an average pCO2 of 450±100 µatm in June–July 2003. At the same time, calculated pCO2 values from previous field campaigns are generally lower than the pCO2 of the Lena River main stem directly measured in this study: 700–800 µatm for the Ust-Kut–Nuya segment (1331 km) and 845–1050 µatm for the Nuya–Aldan segment (1050 km).

Thus, despite the absolute values of calculated pCO2 involving uncertainties (our calculated–measured pCO2 ratio in the Lena River main channel and tributaries equaled 0.67±0.15 (n=47)), this suggests spatial and temporal stability of the pCO2 in the Lena River waters and allows for extrapolation of the measured pCO2 in the Lena River from Yakutsk to Aldan to the lower reaches of the river. As for the Lena tributaries, to the best of our knowledge there is no published information on pCO2 concentration and emission. Overall, the major uncertainty in estimation of the Lena River basin emission stems from a lack of direct pCO2 measurements in the northern part of the main channel over ca. 1000 km downstream of the Aldan River including the large tributary Vilyi. Further, we noted that the largest northern tributary, the Aldan River providing 70 % of the springtime discharge of the Lena River (Pipko et al., 2010), demonstrated sizably higher emissions compared to the Lena River main channel upstream of Aldan (3.2±0.5 and 1.69±0.08 gCm-2d-1, respectively).

For areal emission calculations, we used the range of CO2 emissions from 1 to 2 gCm-2d-1, which covers full variability of both large and small tributaries and the Lena River main channel (Tables 1 and 2, Fig. 2b). This estimation assumes lack of pCO2 dependence on the size of the watershed in the Lena basin as confirmed by our data (Fig. S5 in the Supplement). For an alternative areal emission calculation, we explicitly took into account the water area of the main stem (43 % relative to the total water area of the Lena catchment), and we introduced the partial weight of emission from the three largest tributaries (Aldan, Olekma, and Vitim) according to their catchment surface areas (43 %, 12 %, and 14 % of all sampled territory, respectively). We summed up the contribution of the Lena River main stem and the tributaries, and we postulated the average emission from the main stem upstream of Aldan (1.25±0.30 gCm-2d-1) as representative of the whole Lena River. This resulted in an updated value of 1.65±0.5 gCm-2d-1, which is within the range of 1 to 2 gCm-2d-1 assessed previously. Note that this value is most likely underestimated because emissions from the main stem downstream of Aldan are at least 10 % higher (Table 1, Fig. 1b).

For the 2 months of maximal water flow (middle of May–middle of July), the C emission from the whole Lena basin equates to 2.8±0.85 Tg C, which is 20 % to 30 % of the DOC and DIC lateral export to the Arctic Ocean. Assuming 6 months of open water period and no emission during winter, this yields 8.3±2.5 TgCyr-1 of annual emission for the whole Lena River basin (2 490 000 km2), with a total lotic water area of 28 100 km2. Considering the only 23 200 km2 of water area in July–October (and maximal water coverage in May–June), these numbers decrease by 12 %, which is below the uncertainties associated with our evaluation.

Generally, the SW-to-NE increase in CO2 concentrations and fluxes of the tributaries was consistent with the CO2 pattern in the main stem (Fig. 2; Tables 1 and 2) and thus can be considered a specific feature of CO2 exchange between lotic waters and atmosphere in the studied part of the Lena Basin. At the same time, there were sizable local variations (peaks) in CO2 concentration of the main stem along the sampling route (Fig. 2a). Peaks shown on the diagram of the main stem are not necessarily linked to CO2-rich tributaries but likely reflect local processes in the main stem, including lateral influx from the shores and shallow subsurface waters, which is typical for permafrost regions of forested Siberian watersheds (i.e., Bagard et al., 2011). Given that the data were averaged over a ∼20 km distance, we believe that these peaks are not artifacts but reflect local heterogeneity of the pCO2 pattern in the main stem (turbulence, suprapermafrost water discharge, sediment resuspension, and respiration). Note that such a heterogeneity was not observed in the tributaries, at least at the scale of our spatial coverage (see Figs. S1B and S3).

The PCA demonstrated an extremely low ability to describe the data variability (12 % by F1 and only 3.5 % by F2). We believe that the most likely reason for weak PCA capacity is the rather homogeneous distribution of CO2 and CH4 among the tributaries, primarily linked to the specific hydrological period studied in this work – the spring flood. During this high-flow period, the local lithological and soil heterogeneities among tributaries or the segments of the main stem virtually disappear, and surface flow (via vegetation leaching) becomes the most important driver of riverine chemistry, as is known from adjacent permafrost territories in central Siberia (i.e., Bagard et al., 2011). Nevertheless, some specific features of the data structure could be established. The first factor, significantly linked to pCO2 (0.72 loading), strongly acted on the sample location at the Lena transect, the watershed coverage by deciduous needleleaf forest and shrubs, riparian vegetation, and also the proportion of tundra, bare rock and soils, water bodies, peatland, and bogs (>0.90 loading). This is fully consistent with spatial variation in pCO2 along the permafrost and climate gradient in the main channel and sampled tributaries. Positive loading of riparian vegetation, peatlands, and bogs on F1 (0.927 and 0.989, respectively) could reflect a progressive increase in the feeding of the river basin by mire waters, an increase in the proportion of needleleaf deciduous trees and in the width of the riparian zone from the SW to the NE direction.

Lack of sizable variation in pCO2 between the day and night periods or across the riverbed suggests quite low site-specific and diurnal variability. It may be indicative of a negligible role of primary productivity in the water column given the low water temperatures, shallow photic layer of organic-rich and turbid waters, and lack of periphyton activity during high flow of the spring flood. The pCO2 increased by a factor of 2 to 4 along the permafrost–temperature gradient from the southwest to the northeast, for both the main channel and sampled tributaries. This may reflect a progressive increase in the feeding of the river basin by mire waters, an increase in the proportion of needleleaf deciduous forest, and an increase in the width of the riparian zone. Another strong correlation is observed between the stock of OC in soils (both 0–30 and 0–100 cm depth) and the pCO2 of Lena tributaries. Organic-rich soils are widely distributed in the central and northern parts of the basin. The most southern part of the Lena basin is dominated by carbonate rocks and crystalline silicates in generally mountainous terrain, where only thin mineral soils are developed. The northern (downstream of the Olekma River) part of the basin consists of soils developed on sedimentary silicate rocks as well as vast areas of easily eroded yedoma soils. It is likely that both organic matter mineralization in OC-rich permafrost soils and lateral export of CO2 from these soils, together with particulate and dissolved OC export and mineralization in the water column, are the main sources of CO2 in the river water. Although some studies have demonstrated high lability of dissolved organic matter (DOM) in arctic waters (Cory et al., 2014; Ward et al., 2017; Cory and Kling, 2018), others suggest that DOM photo- and bio-degradation are low and do not support the major part of CO2 supersaturation in water (Shirokova et al., 2019; Payandi-Rolland et al., 2020; Laurion et al., 2021). Note that we have not observed any significant relationship between the DOC and pCO2 in the Lena River and tributaries (Fig. S6A). Lack of such a correlation and absence of diurnal pCO2 variations imply that in-stream processing of dissolved terrestrial OC is not the main driver of CO2 supersaturation in the river waters of the Lena River basin. Furthermore, a lack of lateral (across the riverbed) variations in pCO2 does not support a sizable input of soil waters from the shore, although we admit that much higher spatial coverage along the river shore is needed to confirm this hypothesis.

The role of underground water discharge in regulating pCO2 pattern of the tributaries is expected to be most pronounced in the SW part of the basin (Lena headwaters), where carbonate rocks of the basement would provide sizable amounts of CO2 discharge in the riverbed. However, there was no relationship between the proportion of carbonate rocks on the watershed and the pCO2 in the tributaries (Fig. S6B). Furthermore, for the Lena River main stem, the lowest CO2 concentrations were recorded in the upper reaches (first 0–800 km) where carbonate rocks dominate. Altogether, this makes the impact of CO2 from underground carbonate reservoirs on river water CO2 concentrations unlikely. This is further illustrated by a lack of correlation between pCO2 and DIC or pH (Fig. S7A of the Supplement). The pH did not control the CO2 concentration in the main stem and only weakly impacted the CO2 in the tributaries (Fig. S7B). The latter could reflect an increase in pCO2 in the northern tributaries, which exhibited generally lower pH compared to the SW tributaries hosted within the carbonate rocks. Overall, such low correlations of CO2 with DIC and pH reflected a generally low predictive capacity to calculate pCO2 from measured pH, temperature, and alkalinity (see Sect. 3.4).

Therefore, other sources of riverine CO2 may include particulate organic carbon processing in the water column (Attermeyer et al., 2018), river sediments (Humborg et al., 2010), and riparian zone (Leith et al., 2014, 2015), which require further investigation. In addition, although there was no sizable variation in pCO2 between the day and night periods or across the riverbed, the flux could show different spatial and temporal patterns if k shows larger variability (see Beaulieu et al., 2012). This calls for a need of direct flux measurements in representative rivers and streams of the Lena River basin. Overall, the present study demonstrates highly dynamic and non-equilibrium behavior of CO2 in the river waters, with possible hot spots from various local sources. For these reasons, in situ, high-spatial-resolution measurements of CO2 concentration in rivers – such as those reported for the Lena Basin in this study – are crucially important for quantifying the C emission balance in lotic waters of high latitudes.

The estimated CO2 emissions from the Lena River main channel over 2600 km distance (0.8–1.7 gCm-2d-1) are comparable to values directly measured in rivers and streams of the continuous permafrost zone of western Siberia (0.98 gCm-2d-1; Serikova et al., 2018), the Kolyma River (0.35 gCm-2d-1 in the main stem; 2.1 gCm-2d-1 for lotic waters of the basin), and the Ob River main channel (1.32±0.14 gCm-2d-1 in the permafrost-free zone; Karlsson et al., 2021). At the same time, the Lena River flux (FCO2) values are lower than typical emissions from running waters in the contiguous Unites States (3.1 gCm-2d-1; Hotchkiss et al., 2015), small mountain streams in northern Europe (3.3 gCm-2d-1; Rocher-Ros et al., 2019), and small streams of the northern Kolyma River (6 to 7 gCm-2d-1; Denfeld et al., 2013) and Ob River in the permafrost-affected zone (3.8 to 5.4 gCm-2d-1; Karlsson et al., 2021). In contrast to the main stem, the range of FCO2 in the tributaries is larger (0.2 to 3.2 gCm-2d-1) and presumably reflects a strong variability in environmental conditions across a sizable landscape and climate transect.

Total C emissions from other major eastern Eurasian permafrost-draining rivers (i.e., sum of Kolyma, Lena, and Yenisei rivers) based on indirect estimates (40 TgCyr-1, Raymond et al., 2013) are generally supportive of the estimations of the Lena River in this study (5 to 10 TgCyr-1). At the same time, the C emissions from the Lena River basin (28 100 km2 water area) are lower than those of the lotic waters of western Siberia (30 TgCyr-1 for 33 389 km2 water area; Karlsson et al., 2021). The latter drain through thick, partially frozen peatlands within the discontinuous, sporadic, and permafrost-free zones, which can cause high OC input and processing and, thus, enhanced C emissions (Serikova et al., 2018).

Despite the high uncertainty on our regional estimations (due to lack of directly measured gas transfer values and low seasonal resolution), we believe that these estimations are conservative and can be considered first-order values pending further improvements. In order to justify extrapolation of our data to all seasons and the entire area of the Lena basin, we analyzed data for spatial and temporal variations in pCO2 of the Lena River main stem from available literature. From the literature there were three important findings. First, based on published data, the seasonal and spatial variabilities of pCO2 across the majority of the Lena River main stem are not high during the open water period, although the low reaches of the Lena River may exhibit higher emissions compared to the middle and upper courses (see Sect. 3.4). Second, although small mountainous headwater streams of the tributaries may exhibit high k due to turbulence, this could be counteracted by lower CO2 supply from low OC in mineral soil, lack of riparian zone, and scarce vegetation. Third, although these small streams (watershed area <100 km2) may represent >60 % of total watershed surfaces of the Lena basin (Ermolaev et al., 2018), their contribution to the total water surface is <20 % (19 % from combined analysis of DEM GMTED2010 and 16 % from the GRWL or the global SDG database as estimated in this study). Therefore, given that (i) within the stream–river continuum the CO2 efflux increases only 2-fold, demonstrating a discharge decrease by a factor of 10 000 (from 100 to 0.01 m3s-1; Hotchkiss et al., 2015) and (ii) the watershed area had no impact on pCO2 in the river water (Fig. S5), this uncertainty is likely less important. As such, instead of integrating indirect literature data, we used the pCO2 values measured in the present study to calculate the overall CO2 emission from all lotic waters of the Lena basin.

The C evasion from the Lena basin assessed in the present work is comparable to the total (DOC+DIC) lateral export by the Lena River to the Arctic Ocean (10 TgCyr-1 by Semiletov et al., 2011; or 11 TgCyr-1 (5.35TgDICyr-1+5.71TgDOCyr-1) by Cooper et al., 2008). Moreover, the C evasion strongly exceeds sedimentary C input to the Laptev Sea by all Siberian rivers (1.35 TgCyr-1; Rachold et al., 1996, and Dudarev et al., 2006), the Lena River annual discharge of particulate organic carbon (0.38 Tgyr-1; Semiletov et al., 2011), and OC burial on the Kara Sea shelf (0.37 TgCyr-1; Gebhardt et al., 2005).

Typical concentrations of CH4 in the Lena tributaries and the main channel are 100 to 500 times lower than those of CO2. Given that the global warming potential (GWP) of methane on a 100-year scale is only 25 times higher than that of CO2, the long-term diffuse methane emission from the Lena River basin is still 4 to 20 times lower than that of CO2. However, on a short-term scale (20 years), the GWP of methane can be as high as 96 (Alvarez et al., 2018), and its role in climate regulation becomes comparable to that of CO2. This has to be taken into account for climate modeling of the region.

The follow-up studies of this large heterogenous and important system should include CO2 measurements in (1) the low reaches of the Lena River, downstream of Aldan, where notably large organic-rich tributaries such as Vilyi (454 000 km2) and where the huge flood zone (20–30 km wide) with a large number of lakes and wetlands is developed, and (2) highly turbulent eastern tributaries of the Lena River downstream of Aldan, which drain the Verkhoyansk Ridge and are likely to exhibit elevated gas transfer coefficients.