Magnitude of and Hydroclimatic Controls on CO2 and CH4 Emissions in the Subtropical Monsoon Pearl River Basin

Rivers are important ecosystems for carbon emissions and play a crucial role in the global carbon cycle. However, CO2 and CH4 emissions from subtropical rivers are substantially under‐represented in global‐scale estimates. Here, we explored the regional patterns of riverine CO2 and CH4 dynamics in the Pearl River basin with a subtropical monsoon climate. We found that its CO2 and diffusive CH4 emissions showed a decreasing trend with increasing stream order. Seasonality in CO2 and diffusive CH4 emissions was primarily driven by variations in partial pressure of CO2 (pCO2) and CH4 (pCH4) and gas transfer velocities, which were strongly regulated by hydrology and climate. We further estimated the basin‐wide CO2 and diffusive CH4 fluxes at 17.8 ± 7.4 Tg C yr−1 and 191.5 ± 139.9 Gg C yr−1, respectively. When normalized to the water surface, the mean diffusive fluxes were 790.1 and 8.5 mmol m−2 d−1 for CO2 and CH4, respectively, which were 1.3 and 2.5 times higher than the global mean riverine CO2 and CH4 fluxes, respectively. This suggests that the global significance of subtropical rivers is probably underestimated because their substantially higher CH4 fluxes are unaccounted for. Furthermore, compared with measured pCO2, the alkalinity‐based pCO2 could introduce significant errors by 20% at ∼30% of the sampling sites, underscoring the necessity of direct measurements to reduce uncertainty. This study provides the first estimate of basin‐wide CO2 and diffusive CH4 emissions in the PRB through direct pCO2 and pCH4 measurements, and highlights the role of hydrologic and climatic factors in governing riverine carbon emissions.


Introduction
Streams and rivers are increasingly recognized as a dynamic and significant component of the global carbon dioxide (CO 2 ) and methane (CH 4 ) emissions (Battin et al., 2023;Raymond et al., 2013;Regnier et al., 2022;Rocher-Ros et al., 2023).Recent studies show that the global emissions of CO 2 and CH 4 were 2.0 Pg C yr 1 (Liu et al., 2022) and 20.9 Tg C yr 1 (Rocher-Ros et al., 2023), respectively.However, these estimates are afflicted by large uncertainty, partly due to the limited direct measurements of riverine CO 2 and CH 4 concentrations and the high spatial and temporal heterogeneity in both concentrations and emission (Liu et al., 2022;Raymond et al., 2013;Rocher-Ros et al., 2023).In contrast to lentic waters (e.g., lakes, reservoirs, and ponds), lotic waters (e.g., streams and rivers) receive less attention in CH 4 dynamics, which is largely because of the persistent conventional perception that well-aerated running waters provide unfavorable conditions for CH 4 generation (Campeau et al., 2014;Stanley et al., 2016).Global CH 4 emissions from freshwater ecosystems were estimated only at 1.1 Tg C yr 1 (Bastviken et al., 2011), which is an order of magnitude lower than the latest estimate (Rocher-Ros et al., 2023).This further suggests that more direct measurements of riverine CH 4 emissions are needed to improve our understanding of global greenhouse gas (GHG) emissions.
There are two methods to measure the surface water CO 2 partial pressure (pCO 2 ) in rivers.The first approach (an indirect method) is based on the thermodynamic relationships for equilibria between carbonate, bicarbonate, and aqueous CO 2 , and pCO 2 was calculated from pH and alkalinity (Parkhurst & Appelo, 2013).The other approach is through direct measurements using water-air phase equilibration for headspace technique with discrete water samples or infrared gas analyzers to continuously determine the pCO 2 (Abril et al., 2015).Although equilibrium equations are more commonly used, the calculated pCO 2 is likely overestimated because of the widely distributed acidic, organic-rich streams and rivers, where overestimation could be more than 100% (Abril et al., 2015).This is particularly true for highly polluted Asian rivers with substantial amounts of organic acids being flushed from soils into rivers, a phenomenon that becomes more prominent during the monsoon season (Nayna et al., 2021).Moreover, the accuracy of the indirect method-based pCO 2 relies highly on pH.Uncertainties of the calculated pCO 2 can reach up to ±21% when the field measurements have uncertainties of ±0.1 pH units (Marx et al., 2017).These uncertainties stress the importance of conducting direct measurements of pCO 2 in inland waters.However, the pCO 2 determined from headspace equilibrium can also lead to a high systematic error (up to 300%) if the chemical equilibration of the carbonate system is not properly considered, especially for waters that are highly undersaturated but equilibrated with ambient air (Koschorreck et al., 2021).Consequently, many river ecosystems worldwide still lack credible data on pCO 2 , and little is known about the errors introduced by the alkalinity-based pCO 2 .Owing to the large spatial and temporal variabilities of the pCO 2 and the complex physicochemical characteristics of aquatic environment (Ran et al., 2021;Raymond et al., 2013), studies on pCO 2 in both headwater streams and large rivers should be conducted to strengthen our mechanistic understanding of the differences between alkalinity-based and headspace-based pCO 2 across the full range of river and stream networks.Subtropical regions are characterized by more pronounced seasonal differences between summer (hot and humid) and winter (cool and dry) than tropical regions (Sawakuchi et al., 2014;Yao et al., 2007).Moreover, compared with temperate rivers, the higher temperature in subtropical rivers provides a suitable condition for methanogenesis (Yvon-Durocher et al., 2014) and facilitates increased input of terrestrial CO 2 as a result of enhanced primary productivity (Liu et al., 2021), making subtropical rivers potential hotspots for GHG emissions.With these contrasting hydrologic and climatic conditions, subtropical rivers function as unique ecosystems for GHG emissions in the global context.However, research on CH 4 dynamics in subtropical river ecosystems has received much less attention compared with rivers in other latitudes (Stanley et al., 2023).Furthermore, direct measurements of pCO 2 in subtropical rivers are particularly underrepresented in East Asia when compared with other regions (Liu et al., 2022).East Asia has been one of the most rapidly urbanizing regions in the world over the past few decades, where agricultural and urban-impacted rivers are likely potent GHG emitters (Park et al., 2018).Besides, large quantities of anthropogenic nutrients, coupled with increased nutrient residence time due to dam operation, have substantially enhanced the aquatic primary productivity in East Asia (Han et al., 2018;Park et al., 2018).
The Pearl River is a large subtropical river in South China and the second-largest river entering the South China Sea.The Pearl River basin (PRB) is currently undergoing a series of environmental problems (e.g., water pollution) followed by rapid urbanization and industrialization (Zhang et al., 2009).Although the CO 2 dynamics in the Pearl River have long been reported (Liu & Han, 2021;Yao et al., 2007;Zhang et al., 2009), they were all based on calculated pCO 2 with large uncertainty.To our knowledge, direct measurements of pCO 2 were only reported in two low-gradient streams (Zhang, Li, et al., 2017;Zhang et al., 2021), the Dongjiang River (a tributary of the Pearl River; Liu et al., 2021), and the Pearl River Estuary (Guo et al., 2009).In comparison, studies on CH 4 emissions were restricted to the Pearl River Estuary (Ye et al., 2019).A comprehensive study of the magnitude of CO 2 and CH 4 emissions based on direct measurements in the subtropical monsoon PRB remains poorly explored.In this study, we present the first integrated study of CO 2 and CH 4 concentrations and emissions from the subtropical PRB spanning eight Strahler stream orders.The specific objectives were to: (a) explore the spatial and seasonal patterns of CO 2 and CH 4 concentrations and emissions at the basin scale, (b) assess the reliability of the calculated pCO 2 using the alkalinity-based method in the study area, and finally, (c) estimate the basin-wide CO 2 and diffusive CH 4 fluxes in the PRB and derive their biogeochemical implications for subtropical riverine CO 2 and CH 4 dynamics.Our study provides the first basin-wide observations showing the CO 2 and diffusive CH 4 emissions in the large subtropical monsoon PRB and sheds light on the global significance of CH 4 emissions from subtropical streams and rivers.

Study Area
The Pearl River is the second-largest river in terms of annual discharge and the third-longest river in China, with a drainage area of 4.53 × 10 5 km 2 and eight Strahler orders (Figure 1).There are three large tributaries, including the Xijiang, Beijiang, and Dongjiang rivers, located in the west, north, and east of the PRB, respectively.The relief in the PRB is generally high in the northwest and low in the southeast, with the altitude ranging from ∼0 to 2,800 m (Figure 1; Table S1 in Supporting Information S1).Carbonate rocks are widely distributed in the PRB, especially in the Xijiang River (Table S1 in Supporting Information S1).The upper reach of the Xijiang River is located in the Southeast Asia Karst Region, the world's largest karst area.The PRB is highly affected by monsoons, with about 80% of the annual precipitation falling in the rainy season (April-December).The annual average temperature ranges from 14°C to 22°C, and the annual average precipitation varies in the range of 1,200-2,200 mm across the PRB (Han et al., 2018).
Forest is the dominant land use in the PRB, followed by cropland and grassland (Table S1 in Supporting Information S1).The lower reaches of the three tributaries are mainly located in Guangdong Province, one of the most economically developed regions in China, and are all predominated by urban land uses.In comparison, agricultural land use is prevalent in the upper and middle reaches of the Xijiang River.Reservoirs and dams have been widely constructed in the PRB, especially in the Xijiang River basin that has more than 230 large reservoirs (Han et al., 2018).
distributed in the XJX and LJ watersheds, whereas the NSH and XJH watersheds are primarily underlain by acid plutonic rocks, metamorphics, and carbonate rocks.While agricultural and grassland uses are the major land use types in the XJX watershed, agriculture and forest are the major land use types in the other three watersheds.In addition, urban land use is also important for the LJ and NSH watersheds.

Sampling Strategy and Geospatial Analyses
Sixty-two tributary and mainstem sites covering all the eight Strahler orders of the PRB were sampled from July 19th to August 3rd (wet season) and December 7th to 22nd (dry season) of 2021.These widely distributed streams across the PRB were carefully chosen to reflect the spatial heterogeneity in topography, lithology, hydrology, and land cover within and among regions.Of the 62 sampling sites, 31 sites are located in the mainstream and main tributaries of the Pearl River (Strahler orders 5-8), and the remaining 31 sites are distributed in four small watersheds (Strahler orders 1-5; Figure 1).Delineation of individual sub-watersheds upstream of the sampling sites and estimation of their drainage area (range: 6-308,178 km 2 ; Table S1 in Supporting Information S1) were achieved through a Digital Elevation Model (DEM) with a 30 m resolution (ASTER v3 DEM, NASA et al., 2018) using the spatial analyst tools of ArcGIS 10.2.Stream networks were obtained from the HydroSHEDS database (Linke et al., 2019).The distribution of physiographic characteristics (e.g., lithology and land cover) of the study watersheds was calculated from published geospatial data and delineated sub-watersheds (see details in Table S1 in Supporting Information S1).

Field Sampling and Laboratory Analysis
During the two sampling campaigns, 124 water samples were collected from the middle of streams or from the river bank if the middle is inaccessible.All sampling sites were far away from any visible sewage pollution.River water pCO 2 and pCH 4 were measured by the headspace equilibrium method (see details in Supporting Information S1; Campeau et al., 2014).The theoretical pCO 2 was also determined from pH, water temperature (WT), and alkalinity using PHREEQC version 3 (Parkhurst & Appelo, 2013).The areal emission rate of CO 2 (FCO 2 ) and CH 4 (FCH 4 ) was calculated using a 9.3 L floating chamber at 8 min intervals (0, 8, 16, 24, 32, and 40 min) by collecting 60 mL of gas from the chamber through a syringe and stored in 12-mL Exetainer vials.The rate of gas concentration change within the chamber was utilized to determine the FCO 2 and FCH 4 (Equation S2 in Supporting Information S1; see details in Supporting Information S1).
At each sampling site, we measured WT, dissolved oxygen (DO), pH, and electrical conductivity (EC) using a portable multiparameter probe (Multi 3,420, WTW GmbH, Germany).The pH probe was calibrated using standard pH buffers (4.01, 7.00, and 10.01) prior to measurement, and triple measurements demonstrated a precision of ±0.01 pH units.In addition, alkalinity was determined through triplicate end-point titrations in the field, utilizing 0.02 mol L 1 hydrochloric acid and a mixed indicator comprising bromocresol green and methyl red.More detailed information on water chemistry was described in Supporting Information S1.Wind speed and atmospheric pressure were measured by a handheld anemometer (Kestrel 2500, USA) at 1.5 m above the water surface.Flow velocity was measured using a water flow probe (FP111, USA) with a precision of 0.1 m s 1 .Stream width was measured by a laser rangefinder, and water depth was measured by a sonar fathometer.Sediment grades of the riverbed at each site were recorded following the classification method of Valentine (2019), which includes mud, sand, and gravel.

Basin-Scale Estimation of Annual CO 2 and Diffusive CH 4 Fluxes
The water surface area of the PRB in the wet and dry seasons was determined by multiplying the measured mean stream width with the corresponding stream length derived from the HydroSHEDS database (Linke et al., 2019) for each Strahler order (orders 1-8).To avoid underestimating the stream length by missing the smallest streams, the length of Strahler order 0 streams was estimated by extrapolating the exponential correlation (Figure S1a in Supporting Information S1) between stream order and stream length (Liu et al., 2023;Raymond et al., 2013).The stream width of Strahler order 0 streams was estimated using the same method as the stream length (Figures S1b and S1c in Supporting Information S1).Although intermittent streams play a disproportionately important role in CO 2 emissions (Gómez-Gener et al., 2021), these streams were not considered in this study.The flux error arising from ignoring these intermittent streams is likely minimal because part of the surface area of these intermittent streams has been included in Strahler order 0 streams.Meanwhile, the abundance of intermittent streams in subtropical regions with high runoff, such as the PRB, is relatively small (Liu et al., 2022).
The areal emission rates of diffusive CO 2 and CH 4 in each Strahler order stream were calculated based on the measured pCO 2 , pCH 4 , and gas transfer velocities (k), which were converted from the standardized gas transfer velocity (k 600 ) using the empirical model (Equations S3-S5 in Supporting Information S1; Raymond et al., 2012).These rates were then combined with our estimated water surface area of each stream order to calculate the total fluxes of diffusive CO 2 and CH 4 during the wet and dry seasons in the PRB (Equations S6 and S7 in Supporting Information S1; see details in Supporting Information S1).
Contrary to CO 2 , diurnal variations in CH 4 emissions were not considered in this study due to the lack of studies on a large spatial scale (see details in Supporting Information S1).The total CO 2 and diffusive CH 4 fluxes were normalized to the water surface area and landscape area to calculate the area-weighted fluxes.We also calculated the CO 2 equivalents (CO 2 -eq) of CH 4 by assuming that CH 4 has a 28 times stronger global warming potential than CO 2 over a 100-year period (Ciais et al., 2014).Uncertainties in CO 2 and CH 4 emission fluxes were determined using Monte Carlo simulations that ran 10,000 iterations.The Monte Carlo analysis was conducted for streams grouped by Strahler orders and sampling seasons, considering the uncertainties associated with riverine pCO 2 and pCH 4 , k values, and water surface area.During each iteration, parameters were randomly resampled from normal distributions constrained by the mean and standard deviation (SD).The uncertainties obtained from the Monte Carlo analysis were reported as the 1δ deviation of the simulated emission magnitude distributions.

Statistical Analysis
The Shapiro-Wilk test was used to examine the normality of the data.One-way ANOVA with Tukey's post-test, Mann-Whitney U test, and Kruskal-Wallis test followed by Holm's Stepdown Bonferroni correction were performed for comparison of distributions between two or multiple groups by using SPSS 26.Simple linear regressions were applied using Origin (Pro) 2021 to assess the relationship between measured pCO 2 and alkalinitybased calculated pCO 2 , predict the calculation error of pCO 2 using pH, and explore the correlations between pCO 2 , pCH 4 , WT, and DO.Values are presented as median ± SD.All statistical tests were carried out at a 0.05 significance level.Because aquatic CO 2 and CH 4 concentrations and fluxes would be greatly influenced by outliers, median values are a better choice to represent the data range rather than means (Hutchins et al., 2019;Stanley et al., 2023).

Spatial and Temporal Variations in Water Quality Variables
The water temperature varied from 20.0 to 35.3°C with a median of 30.1°C in the wet season and from 13.4 to 21.2°C with a median of 18.2°C in the dry season (Table 1).In general, river water was mildly alkaline, with the pH increasing from 6.66 to 8.92 (median: 7.77) in the wet season and from 6.53 to 8.51 (median: 7.92) in the dry season.Conductivity was slightly higher during the dry season, with a median of 286 and 295 µS cm 1 for the wet and dry seasons, respectively.Alkalinity was similar in both seasons but varied in a wide range (varied from 359 to 3,838 μmol L 1 with a median of 2,040 μmol L 1 in the wet season and from 483 to 4,385 μmol L 1 with a median of 2,113 μmol L 1 in the dry season).All sites were significantly less oxygenated in the wet season (median: 7.0 mg L 1 ) than in the dry season (median: 9.1 mg L 1 ).

Spatial and Temporal Variations in Riverine CO 2 and CH 4 Dynamics
The riverine pCO 2 in the wet season varied from 146 to 6,362 μatm with a median of 2,789 μatm (n = 62), which is significantly higher than the pCO 2 level in the dry season (median: 1,351 μatm; p < 0.01; Table 1).In total (n = 124), approximately 97% of the measurements had the pCO 2 higher than the atmospheric equilibrium (∼414 μatm).Samples with pCO 2 lower than the atmospheric equilibrium were all super-saturated in DO (i.e., higher than 100%), and the sampling sites are all located within 15 km downstream of dams.The riverine pCH 4 in all streams was higher than the atmospheric pCH 4 (∼1.87 μatm).The pCH 4 varied by four orders of magnitude, ranging from 14 to 11,119 μatm (a highly polluted urban stream in the LJ catchment), with a median of 495 μatm in the wet season.In comparison, the median pCH 4 in the dry season (168 μatm) was substantially lower than the wet season.There was a decreasing trend of pCO 2 and FCO 2 with increasing stream order (especially for stream orders 2-7; Figure 2).Second-order streams exhibited the highest median pCO 2 at 4,377 and 2,881 μatm in the wet and dry seasons, respectively.The median pCO 2 gradually decreased to 1,669 and 752 μatm in the eighth-order streams in the wet and dry seasons, respectively.In contrast, pCH 4 and FCH 4 showed no discernible trend with stream order (Figure 3).However, similar to CO 2 , the second order streams exhibited the highest pCH 4 and FCH 4 , with a median of 1,858 and 522 μatm for the pCH 4 in the wet and dry seasons, respectively, and a median of 19.78 and 1.19 mmol m 2 d 1 for the FCH 4 in the wet and dry seasons, respectively.We also found a gradual decrease of pCO 2 with increasing stream width in both seasons (Figures S2a and S2b in Supporting Information S1), but there was no significant trend between pCH 4 and stream width (Figures S2c and S2d in Supporting Information S1).Additionally, stream water pCH 4 did not show significant differences across various sediment grades (Figure 4).Furthermore, there were weak but significantly positive correlations between WT and stream water pCO 2 and pCH 4 (p < 0.0001; Figures 5a and 5b).In comparison, DO was significantly negatively correlated with pCO 2 and pCH 4 (p < 0.0001; Figures 5c and 5d).The slope of the linear regression between headspace-based pCO 2 and modeled pCO 2 using alkalinity was 1.02 for all samples (n = 124; Figure 6a).The mean ratio between modeled to measured pCO 2 was 0.95 (±0.20; Figure 6b).For individual sites, however, the ratio varied widely in the range of 0.37-1.53.In total, 28% of the modeled pCO 2 values showed underestimation or overestimation of more than 20%.A greater magnitude of underestimation tends to occur when river water pH is higher than 8 (Figure 6b).

Basin-Wide Estimates of CO 2 and Diffusive CH 4 Fluxes
The water surface area of the stream network in the PRB was 5,220 km 2 in the wet season and 5,063 km 2 in the dry season (Figure S3 in Supporting Information S1).Total riverine CO 2 emissions were estimated at 17.8 ± 7.4 Tg C yr 1 , with CO 2 emission during the wet season (14.2 ± 6.4 Tg C) nearly three times higher than that in the dry season (4.8 ± 3.3 Tg C).Moreover, the total riverine CH 4 emissions were estimated to be 191.5 ± 139.9 Gg C yr 1 , with the CH 4 emission fluxes in the wet and dry seasons at 158.8 ± 139.2 Gg C and 46.5 ± 27.6 Gg C, respectively.When expressed as CO 2 -equivalents, the total flux was 23.2 Tg CO 2 -eq yr 1 , with a dominant contribution from CO 2 (77%).The FCO 2 /FCH 4 ratio (in CO 2 -eq), varying from 1.8 to 4.9, does not exhibit any detectable trend with stream order (Figure 7).When normalized to the water surface area, the diffusive fluxes were 790.1 and 8.5 mmol m 2 d 1 for CO 2 and CH 4 , respectively.Similar to the in situ measured CO 2 fluxes, the extrapolated CO 2 fluxes in the PRB showed a decreasing trend with increasing stream order (Figure 7).Consequently, headwater streams (0-2) contributed to 75% of the total CO 2 fluxes, despite that they accounted for only 31% of the total water surface area.In contrast to the in situ measured diffusive CH 4 fluxes, the extrapolated  diffusive CH 4 fluxes also significantly decreased with increasing stream order (R 2 = 0.85, p < 0.0001), with headwater streams (0-2) contributing to 72% of the total diffusive CH 4 fluxes.

Spatial Patterns in CO 2 and CH 4 Concentrations and Fluxes
Riverine pCO 2 is typically highest in headwater streams where hydrological flow paths are well connected with CO 2 -rich groundwaters and riparian soils (Marx et al., 2017).The high pCO 2 in headwater streams, coupled with fast gas transfer velocities in mountainous regions, resulted in rapid CO 2 outgassing and thus the high FCO 2 in low-order streams and the decreasing pCO 2 along the river course (Figure 2).This is consistent with previous studies conducted in other climatic regions (e.g., Butman & Raymond, 2011;Campeau et al., 2014;Hutchins et al., 2019;Ran et al., 2021) and the Yangtze River (Ran et al., 2017), which shares a similar subtropical monsoon climate as the PRB.Notably, the pCO 2 levels remained relatively constant in downstream large rivers (i.e., Strahler order 6-8) located in the lower reaches of the Yangtze River Basin that flow through the low-gradient landscapes (Ran et al., 2017).However, even in the lower reaches of the PRB, the pCO 2 in large rivers (i.e., Strahler order 6-8) exhibited a decreasing trend as the stream order increased (Figure 2).This trend is likely caused by the gradual reduction in river-groundwater hydrological connectivity, which can be attributed to the prevalence of mountains and hills across the PRB (Figure 1).These mechanisms that lead to the decreasing pCO 2 and FCO 2 with stream order can also explain the declining pCO 2 with increasing stream width (Figure S2 in Supporting Information S1).Apart from the influence of hydrological conditions, nutrient availability probably also contributed to the decreasing trend of pCO 2 with increasing stream order.Both dissolved total nitrogen (TN) and total phosphorus (TP) exhibited a decreasing trend with increasing stream order in both the wet and dry seasons (Figures S4a and S4b in Supporting Information S1), and a similar trend for dissolved organic carbon (DOC) displayed in the wet season (Figure S4c in Supporting Information S1).Higher nutrient and DOC loading can enhance the production of GHGs (Park et al., 2023) in lower-order streams, illustrating the anthropogenic impact on GHG emissions, as evidenced by the positive correlation between catchment population density and pCO 2 , as well as pCH 4 (Figure S5 in Supporting Information S1).
In contrast to pCO 2 , there were no apparent changes in pCH 4 with stream order and stream width (Figure 3 and Figure S2 in Supporting Information S1), despite the fact that higher nutrient supply and relatively lower DO levels in lower-order streams (Figure S6 in Supporting Information S1) provide a favorable environment for CH 4 production.However, this does not imply that the spatial distribution of pCH 4 was not affected by anthropogenic activities (Figure S5b in Supporting Information S1).This is likely due to the high coverage extent of and connectivity with wetlands (Figure S7 in Supporting Information S1), which is generally associated with high CH 4 concentrations (Borges et al., 2019;Zhang, Zimmermann, et al., 2017).Consequently, higher-order streams tend to exhibit high CH 4 production rates, potentially masking any decreasing trend of pCH 4 with stream order.The differences in the distribution patterns of CO 2 and CH 4 indicate that the controlling mechanisms of the two gases were different.Although both gases share the same sources from soils, groundwater (Lupon et al., 2019), and the processing of organic matter (Campeau & Del Giorgio, 2014), dissolved CO 2 is primarily regulated by the pH-dependent reaction equilibrium among inorganic carbon species (Marx et al., 2017;Stets et al., 2017).This pH-related effect is known as carbonate buffering, and it is most pronounced in waters with high alkalinity (Stets et al., 2017), such as karst rivers in the PRB.Moreover, CH 4 emissions did not show significantly higher fluxes at sites with fine sediment (Figure 4) as previously reported (e.g., Sawakuchi et al., 2014;Tang et al., 2021).A large volume of fine sediment deposits in the streambed can create an anoxic habitat conducive to methane production (Zhu et al., 2022), and the delivery of fine sediment has been found to be closely correlated with increases in riverine DOC induced by anthropogenic activities, further supporting the heightened methane emissions (e.g., Tang et al., 2021;Zhu et al., 2022).However, we did not find significant differences in riverine DOC concentrations among the three sediment grades (figure not shown), resulting in the insignificant effect of fine sediment on increasing CH 4 emissions in the PRB.This was also likely due to the large spatial variability of landscapes across the PRB that drives great changes in gas transfer velocities and methane production rates (Crawford et al., 2017;Hutchins et al., 2019), thereby masking the impacts of sediment grade.
The PRB spans a wide range of landscape features (e.g., land use types/covers, lithology, and elevation) and climate, which results in significant differences in water chemistry and CO 2 and CH 4 dynamics (Table 1).The median riverine pCO 2 (1,715 μatm) in the PRB was lower than the global median (∼2,304 μatm) (Stanley et al., 2023).Consequently, the riverine CO 2 fluxes (median: 51 mmol m 2 d 1 ) measured through floating chambers were significantly lower than the global median value (128 mmol m 2 d 1 ).In comparison, while the median pCH 4 (289 μatm) was two times the global median value (∼141 μatm), the corresponding diffusive CH 4 fluxes (median: 0.41 mmol m 2 d 1 ) were quite close to the global median (0.44 mmol m 2 d 1 ) (Stanley et al., 2023).There are probably two reasons for the lower CO 2 concentrations and fluxes in the PRB compared to the global median.The observations in the global data set were primarily collected in summer when dissolved CO 2 concentrations and fluxes were high due to larger terrestrial carbon inputs into drainage networks (Liu et al., 2022;Stanley et al., 2023).Furthermore, the evasion of CO 2 in the PRB may have been substantially impacted by primary production in karst rivers, which resulted in a low evasion rate and even the lowest of all reported rivers worldwide (Zhang, Li, et al., 2017).This was further validated by the significant negative correlation between DO and pCO 2 (R 2 = 0.68, p < 0.0001), a relationship that is commonly interpreted as evidence for the crucial role of aquatic photosynthesis and respiration in regulating riverine CO 2 dynamics (e.g., Chen, Zhong, et al., 2021;Pu et al., 2017).

Hydrologic and Climatic Controls on CO 2 and CH 4 Concentrations and Fluxes
The seasonal pCO 2 and pCH 4 dynamics, as shown in Table 1, were likely linked to changes in water temperature, which was significantly different between the wet and dry seasons.The reduced gas solubility due to increased temperature in the wet season could lead to enhanced aquatic GHG evasion from surface waters (Dinsmore et al., 2013).In addition, the higher temperature in the wet season is an important factor in controlling riverine pCO 2 and pCH 4 dynamics by influencing aquatic primary productivity and respiration (Ludwig et al., 2022), promoting methanogenesis (Yvon-Durocher et al., 2014), and enhancing terrestrial microbial and vegetation productivity (Dinsmore et al., 2013), thereby resulting in higher GHG fluxes in the wet season.Particularly, the weak positive correlations between riverine pCO 2 and pCH 4 and water temperature (Figure 5) also suggest the temperature/climatic regulation on pCO 2 and pCH 4 .Moreover, the seasonality of precipitation and subsequent changes in discharge and groundwater inflows are also significant determinants of the seasonal trends of GHG dynamics (Lupon et al., 2019), given the large seasonal variations in precipitation and discharge within the PRB (Han et al., 2018).We observed a significant positive correlation between runoff and pCO 2 (p < 0.0001; Figure S8a in Supporting Information S1).This is consistent with previous studies which demonstrate that increasing baseflow with large inputs of soil CO 2 in the early wet season can produce substantially higher pCO 2 in the Pearl River (Yao et al., 2007;Zhang et al., 2009).In addition, enhanced surface turbulence tends to increase gas transfer velocity (the k 600 was significantly higher in the wet season than in the dry season, Table 1; p < 0.01, Mann-Whitney test), which, together with the higher pCO 2 , led to the higher FCO 2 in the wet season (Table 1).The median FCO 2 was 445% higher in the wet season than in the dry season, revealing a significant difference in seasonal CO 2 emissions, which further highlights hydrology as a vital influencing factor in determining riverine pCO 2 dynamics (Liu et al., 2022;Marx et al., 2017).
Compared with the relatively weak impact of water temperature, pCO 2 and pCH 4 were strongly regulated by DO (Figures 5c and 5d), especially for CO 2 (R 2 = 0.66).DO is an essential indicator for river network metabolism (Battin et al., 2023), and it typically exerts a negative effect on riverine pCO 2 and pCH 4 (Borges et al., 2015;Ludwig et al., 2022).Aquatic photosynthesis and respiration produce and consume DO, respectively, with a low DO level denoting anoxic conditions favorable for methanogenesis (Anthony et al., 2012;Ludwig et al., 2022).The considerably higher DO levels during the dry season (Table 1) can be attributed to several factors.These include increased DO solubility resulting from cooler water temperature, reduced exchange with atmospheric oxygen owing to decreased water surface turbulence, and enhanced aquatic photosynthesis facilitated by low turbidity, high light transmissivity, and prolonged water retention in slowly flowing waters (Piatka et al., 2021).The higher DO levels in the dry season have likely contributed to the significantly lower pCH 4 due to the oxygenated environments, which are unsuitable for CH 4 production.Likewise, the enhanced aquatic photosynthesis with weakened microbial respiration in the dry season has also contributed to the lower pCO 2 (Campeau & Del Giorgio, 2014).Thus, both pCO 2 and pCH 4 and emission fluxes exhibited a strong seasonal variability in all rivers, with the median concentrations and fluxes in the wet season being two times higher than those in the dry season (Table 1).In short, DO and water temperature demonstrated the effects of stream metabolism, methanogenesis, and methane oxidation on CO 2 and CH 4 dynamics in the PRB.
Contrary to the temporal variation in CO 2 dynamics, seasonal changes in riverine CH 4 have rarely been reported worldwide.Prior studies have observed an inverse relationship between discharge and pCH 4 levels (e.g., Anthony et al., 2012;Sawakuchi et al., 2014).This inverse relationship is largely attributed to a higher CH 4 evasion rate under high flow conditions due to enhanced surface turbulence, resulting in lower CH 4 concentrations in the river waters (Campeau & Del Giorgio, 2014).Additionally, the dilution of dissolved CH 4 by discharge (Anthony et al., 2012;Sawakuchi et al., 2014), and the limited CH 4 production due to the prolonged time of CH 4 oxidation in deeper water columns during high flow periods (Sawakuchi et al., 2014) can also contribute to this inverse relationship.However, Lupon et al. (2019) found a positive correlation between pCH 4 and discharge in a boreal stream, which was attributed to a greater groundwater CH 4 contribution during high-flow periods.Similarly, we discovered a significant increasing trend of pCH 4 with elevated runoff (p < 0.0001; Figure S8b in Supporting Information S1).However, when the riverine pCH 4 levels are exceptionally high (e.g., >2,000 μatm at some sites in the LJ catchment), its relationship with runoff no longer follows the positive correlation, which is probably due to anthropogenic influences (Figure S8b in Supporting Information S1).This suggests that a flow threshold may exist in controlling CH 4 production and evasion.Similar to CO 2 , we observed a substantially higher diffusive CH 4 flux in the wet season than in the dry season (Table 1), which is in agreement with the considerably higher pCH 4 in the wet season than in the dry season.The driving mechanisms are consistent with the findings by Lupon et al. (2019), indicating the need for a higher sampling frequency to reduce the prediction error of CH 4 fluxes in river networks.

Differences Between Headspace-Based pCO 2 and Alkalinity-Based pCO 2
Previous studies on riverine pCO 2 in the Pearl River were largely determined by the indirect alkalinity-based method (e.g., Liu & Han, 2021;Zhang, Li, et al., 2017;Zhong et al., 2018).For karst rivers and streams, such as these in the Xijiang River basin, that are typically characterized by high ionic strength, high pH, and low DOC concentrations, the calculation errors of pCO 2 by this method are relatively low (Abril et al., 2015;Liu et al., 2020).However, it remains necessary to quantify the degree of accuracy of the estimated pCO 2 in these rivers to refine the flux estimates of riverine CO 2 emissions.Our study showed that the overall pCO 2 in the PRB is slightly underestimated (by 5%) if it is calculated by the alkalinity-based method.Nevertheless, this method can produce considerable overestimations (e.g., by 153% at site XJ3 in the mainstream of the Xijiang River) and underestimations (e.g., by 63% at site ZJ2 in the mainstream of the Beijiang River) at certain locations.In addition, approximately 30% of the modeled pCO 2 values exhibited an estimation error of more than 20%, which demonstrates that the alkalinity-based method is not applicable to the rivers in the Pearl River basin, even to the Xijiang River where karst rivers are widely distributed.
Based on the linear relationship between pH and the ratio between modeled to measured pCO 2 , we further evaluated the most suitable pH range for using the alkalinity-based method.For estimation errors within 5% and 10%, the pH range was 7.38-7.79and 7.17-8.00,respectively (Figure 6b).However, water samples with the pH ranging from 7.17 to 8.00 accounted for only 56% of the total in the PRB (n = 124), suggesting the difficulty of applying this technique to determine the riverine pCO 2 .Moreover, it should be noted that in other rivers with low alkalinity and higher DOC concentrations (Abril et al., 2015;Liu et al., 2020), the pCO 2 errors from this approach will be even larger (e.g., +350% when total alkalinity <500 μmol L 1 ; Abril et al., 2015) and the computed pCO 2 results are thus unreliable.Therefore, direct measurement of pCO 2 in most rivers using portable probes or the headspace equilibrium method is highly recommended to constrain the error to be <10%.

Regional and Global Significance of the Carbon Emissions From the PRB
The areal CO 2 fluxes in the PRB (mean: 790.1 mmol m 2 d 1 ) were higher than the global average of 594 mmol m 2 d 1 (Liu et al., 2022) and the temperate rivers of the conterminous United States (541 mmol m 2 d 1 ; Butman & Raymond, 2011), and even higher than tropical rivers (735 mmol m 2 d 1 ; Liu et al., 2022).Unexpectedly, the CO 2 fluxes (mean: 212 mmol m 2 d 1 ; Ran et al., 2021) in the Greater Pearl basin (a region including the PRB and adjacent subtropical rivers) estimated from water quality data were substantially lower than our results, further highlighting the significance of direct measurement of CO 2 emissions and the need for high-frequency sampling.In contrast to CO 2 fluxes, the mean diffusive CH 4 flux in the PRB (8.5 mmol m 2 d 1 ) was 2.5 times higher than the global mean diffusive flux (3.4 mmol m 2 d 1 ; Rocher-Ros et al., 2023), due largely to the warmer climate, high population densities, and strong river regulation, which are all common characteristics of (sub)tropical rivers (Park et al., 2018;Stanley et al., 2023).This suggests that current global significance of CH 4 emissions from subtropical river networks is probably underestimated (Rocher-Ros et al., 2023).The FCO 2 /FCH 4 (diffusive CH 4 flux was expressed in CO 2 -eq) ratios (mean: 3.1; range: 1.8-4.9; Figure 7) in the PRB were significantly lower than previous studies in tropical rivers (e.g., 11;Borges et al., 2015), temperate rivers (e.g., 6-12;Galantini et al., 2021), alpine permafrost rivers (e.g., 23; Zhang et al., 2020), and high latitude rivers (e.g., 140; Striegl et al., 2012).The lower FCO 2 /FCH 4 ratios in the PRB further challenge the conventional view that CH 4 emissions play a negligible role in GHG emissions from river ecosystems (Dahm et al., 1991), let alone the ebullitive CH 4 fluxes that were unaccounted for in this study.The unexpectedly lower ratios also reflect the higher CH 4 emission rates and the more widespread flooded areas in the PRB, which serve as hotspots for CH 4 production and emission (Borges et al., 2015).This is consistent with the spatial patterns of FCO 2 (a decreasing trend) and FCH 4 (no discernible trend) with the increasing stream order.Consequently, the flooded areas typically observed in high-order streams showed lower FCO 2 /FCH 4 ratios.
For the entire PRB, low-order headwater streams (0-2) contributed to more than 70% of the total CO 2 and CH 4 emissions, suggesting the disproportionate role of headwater streams in basin-wide carbon emissions (Rocher-Ros et al., 2023).This also indicates that the spatial variability in diffusive CH 4 fluxes was mainly controlled by landscape-driven gas transfer velocity (i.e., k 600 ) given that pCH 4 was not significantly higher in low-order streams.Clearly, this is different from CO 2 emissions, with the pCO 2 in low-order streams significantly higher than that in high-order streams as discussed earlier, which is an important reason for the higher CO 2 fluxes in low-order streams.Yet, it must be pointed out that the higher gas transfer velocities in low-order streams are also crucial for maintaining their higher CO 2 fluxes (Butman & Raymond, 2011;Marx et al., 2017).
For the water surface area of the PRB, it is worth noting that the magnitude of its seasonal fluctuations is only 3.0%, similar to that in the Dongjiang River (Liu et al., 2023).This is probably because of the strong flow regulation resulting from dam operations in the PRB.Such regulation has remarkably reduced variations in stream width, which is an important factor influencing riverine carbon emissions yet rarely considered in previous studies.The substantially reduced flow velocity due to damming would further weaken water surface turbulence, leading to reduced gas transfer velocities and, subsequently, carbon emissions across the water-air interface (Ni et al., 2022).Therefore, the seasonal variations in basin-wide CO 2 and diffusive CH 4 fluxes were primarily regulated by seasonal changes in pCO 2 and pCH 4 as well as gas transfer velocities.
Undoubtedly, our basin-wide flux estimates of CO 2 and CH 4 emissions were likely conservative.First, our sampling sites are mostly located near watershed outlets with relatively gentle topography that is characterized by consistently lower flow velocities compared with upstream steep channels, resulting in distinctly lower k 600 results than the values computed (Figure S9 in Supporting Information S1) using the models developed by Raymond et al. (2012).This finding aligns with prior studies conducted in the Yangtze River (Liu et al., 2017).This also explains why our estimated basin-wide emission rate (Section 3.4) holds greater global significance than the measured site-specific emission rate (Section 3.1).However, this is unavoidable in the study of large river systems because it is often challenging to perform in situ measurements at sites with steep slopes or under turbulent flow conditions (Borges et al., 2015;Liu et al., 2023).Second, ebullition is an important pathway for CH 4 emissions and the dominant pathway in some river systems (e.g., Aben et al., 2017;Crawford et al., 2014), especially in rivers with eutrophic environments (Park et al., 2023;Yang et al., 2024).For instance, ebullition can account for up to 99% of the total CH 4 flux in eutrophic urban rivers (Chen, Wang, et al., 2021).Similar to CO 2 fluxes, the inherent diel and seasonal variations in CH 4 ebullition further complicate flux estimation (Chen, Wang, et al., 2021;Sawakuchi et al., 2014).Due to the lack of reliable and widely applicable models in predicting the ebullitive CH 4 flux in large rivers, we did not quantify CH 4 ebullition in this study.Future research is needed to examine the spatiotemporal patterns of CH 4 ebullition and their underlying processes in the PRB.Furthermore, the use of floating chambers might be problematic by altering the natural state of flowing waters, leading to considerable errors in the computed areal emission rates (Campeau et al., 2014;Zheng et al., 2022).For large river basins such as the PRB, these errors may cause biases in flux upscaling due to the limited number of floating chamber deployments and the spatial heterogeneity in carbon emissions.

Conclusions
This research is the first study to analyze the spatial and temporal patterns in riverine CO 2 and CH 4 concentrations and emissions in the large subtropical monsoon Pearl River basin and to estimate the basin-wide CO 2 and diffusive CH 4 fluxes based on upscaling of in situ measurements across the PRB.Our results show a high spatial and temporal heterogeneity in both the concentrations and fluxes of riverine CO 2 and CH 4 , but with distinctive spatiotemporal patterns.There was a decreasing trend in pCO 2 and FCO 2 with increasing stream order, while pCH 4 and FCH 4 displayed no discernible trend with stream order.Both dissolved CO 2 and CH 4 concentrations and fluxes were significantly higher in the wet season than in the dry season.Hydrology, water temperature, and DO were identified as primary regulators of the seasonal variations in pCO 2 and pCH 4 , highlighting hydrologic and climatic controls on riverine GHG emissions, which have important biogeochemical implications in the context of global climate change.Based on basin-wide extrapolation, headwater streams (Strahler orders 0-2) contributed to 75% of the total emissions in terms of greenhouse warming potential.The areal CO 2 and diffusive CH 4 fluxes in the PRB are slightly higher (1.3 times) and significantly higher (2.5 times) than the global mean CO 2 and CH 4 fluxes, respectively.However, our flux estimates of the basin-wide GHG emissions are likely conservative due largely to their huge spatial and temporal heterogeneity.Further studies are warranted to integrate CH 4 ebullition into regional GHG emission estimates, which is probably a significant pathway of CH 4 emissions in subtropical rivers.This is particularly possible for river basins undergoing rapid urbanization and intensive agricultural activities.In addition, sampling with higher frequency in future upscaling efforts will certainly improve the basin-wide flux estimates.

Figure 1 .
Figure 1.Location of the sampling sites (n = 62) in headwater streams (Nanshanhe River, Liujiang River, Xijiuxi River, and Xiaojianghe River) and along large rivers (the Xijiang River, Beijiang River, and Dongjiang River) of the Pearl River basin.See TableS1in Supporting Information S1 for more information.

Figure 2 .
Figure 2. Box-and-whisker plots showing (a) pCO 2 and (b) CO 2 emission rate (FCO 2 ) by Strahler order in the wet and dry seasons.The box represents the 25th and 75th percentiles, the open square and horizontal line represent the mean and median, respectively, and the whiskers represent 1.5 times the upper and lower interquartile ranges (IQR).The solid dots denote outliers.

Figure 3 .
Figure 3. Box-and-whisker plots showing (a) pCH 4 and (b) diffusive CH 4 emission rate (FCH 4 ) by Strahler order in the wet and dry seasons.The box represents the 25th and 75th percentiles, the open square and horizontal line represent the mean and median, respectively, and the whiskers represent 1.5 times the upper and lower interquartile ranges (IQR).The solid dots denote outliers.

Figure 4 .
Figure 4. Box-and-whisker plots showing the pCH 4 by sediment grades in the (a) wet season and (b) dry season.The box represents the 25th and 75th percentiles, the open square and horizontal line represent the mean and median, respectively, and the whiskers represent 1.5 times the upper and lower interquartile ranges (IQR).The solid dots denote the outliers.The letters above the boxes represent significant differences between the grouping of sediment grades at the significance level of 0.05.

Figure 5 .
Figure 5. Stream water pCO 2 and pCH 4 as a function of (a, b) water temperature and (c, d) dissolved oxygen (DO).Outliers, values that are 1.5 × IQR greater than the third quartile, were excluded from linear regression analyses (solid red line).

Figure 6 .
Figure 6.(a) Comparison between measured pCO 2 based on the headspace method and modeled pCO 2 using alkalinity, (b) pH as a good indicator to constrain the error of modeled pCO 2 , as shown by the ratio of modeled and measured pCO 2 versus pH.The black horizontal line in panel (b) represents the ratio of 1, and the baby pink and navajo-white bands represent the 90% and 95% precision of the estimates, respectively.

Table 1
Water Chemistry Characteristics of the Study Streams and Rivers in the PRB