Nonlinear CO₂ degassing dynamics in the Lijiang River Basin of the World Heritage Site

Abstract

As a core component of the South China Karst World Heritage site, carbon dynamics in the Lijiang River Basin are crucial for ecosystem conservation. This study quantified spatiotemporal variations in CO₂ degassing fluxes (FCO₂) across Strahler order rivers in June and December 2019. FCO₂ exhibited a nonlinear relationship with river order: increasing with order in June but decreasing in December. This shift is likely influenced by respiration and organic carbon degradation (June), as well as photosynthesis and carbonate weathering (December), respectively. Gas transfer velocity and terrestrial carbon input caused FCO₂ trends to deviate from expectations at specific orders. In addition, lower-order streams (orders 1–3), covering 34% of the basin area, contributed 38% of total emissions, challenging the hypothesis of disproportionately high emissions from small streams. Linking karst heritage protection to riverine carbon cycling, this study aids carbon emission control, water conservation, and ecosystem stability in the World Heritage site.

Introduction

The ecological fragility of karst World Natural Heritage sites highlights the exceptional conservation value of these areas¹. As the core zone of the World Natural Heritage Site of South China Karst, the Guilin karst landscape not only showcases a concentration of geological wonders but also embodies the essence of its landscape ecosystems through the Lijiang River Basin². In this context, accurately monitoring CO₂ emissions in the Lijiang River Basin is of great significance. This monitoring not only provides an essential scientific basis for karst ecological protection but also enables dynamic analysis of the carbon cycle, serving as an early warning for ecological imbalance risks and thereby safeguarding basin ecosystem stability¹. The necessity of such precise quantification is not limited to regional protection but is also closely related to the key role rivers play in the global carbon cycle. Rivers function as critical biogeochemical hubs³, actively connecting terrestrial, marine, and atmospheric carbon reservoirs and exerting a vital influence on carbon fluxes at both regional and global scales^4,5. As rivers transport carbon from terrestrial to marine ecosystems, some of this carbon is fixed, stored, and subsequently released as CO₂⁶. Global CO₂ emissions from rivers are estimated at 2.0 ± 0.2 Pg C yr^−1 4,7, constituting 85% of total CO₂ emissions from inland waters⁸. Consequently, rivers represent a major source of atmospheric CO₂, making the quantification of their emissions, as undertaken here for the Lijiang River, indispensable for accurately constraining the global carbon budget.

Riverine CO₂ emissions are a complex and dynamic biogeochemical process with significant spatial and temporal heterogeneity, which poses a challenge in accurately quantifying these emissions⁷. While much attention has been given to the temporal dynamics of riverine CO₂ degassing flux (FCO₂)^8,9, studies on its spatial variability still face significant limitations¹⁰. Existing spatial analyses are often restricted to a single scale, such as latitudinal gradients comparisons^11,12, mainstem and tributary streams within a watershed^13,14, or upstream and downstream streams comparisons¹⁵, and have not yet systematically revealed the coupling mechanism between river Strahler order and FCO₂. This mechanism is an important framework for characterizing the structure of hydrological networks and is crucial for clarifying the spatial distribution patterns of carbon emissions. Therefore, studying the characteristics of carbon emissions dependent on river order is conducive to constructing a global river CO₂ flux model and improving the accuracy of global-scale estimates.

Most current studies on the dynamic relationship between river order and FCO₂ focus on large-scale analyses. For example, studies on the relationship between river order and FCO₂ in regions such as the Pearl River Basin¹⁶, inland waters of China¹⁷, continuous waters of the United States¹⁸, and global river ecosystems¹⁹ have found that FCO₂ generally decreases significantly with increasing river Strahler order. FCO₂ was significantly higher in headwater and mountain streams compared to larger rivers, primarily due to higher gas transfer velocities (k values)^19,20,21,22, and this elevated FCO₂ is particularly pronounced in headwater streams also due to the steep partial pressure of CO₂ (pCO₂) gradient at water-air interface, which results from abundant carbon sources, especially organic and inorganic carbon in the Arctic and karst regions^23,24,25. However, at the scale of a single watershed, the relationship between river Strahler order and FCO₂ may be nonlinear²⁶. Because watershed FCO₂ is influenced by a range of complex, coupled biological, physical, and chemical processes, leading to considerable spatial variability^13,18,27,28. For example, in the Furong River, the FCO₂ of the main stream is higher than that of the smaller tributary Chiwuxi River, due to carbonate weathering and aquatic metabolic processes^23,29. Conversely, in the Xijiang River Basin, the FCO₂ of tributaries is significantly higher than that of the main stream, owing to differences in pCO₂ and k values^30,31. In addition, no significant difference in FCO₂ is observed between large and small tributaries in the Dongjiang River Basin, due to the influence of terrestrial carbon inputs and river aquatic metabolism processes³². In summary, the relationship between river Strahler order and FCO₂, along with its influencing factors, remains unclear at the scale of a single watershed. This uncertainty presents a significant challenge to the study of riverine FCO₂, underscoring the need for further exploration of the relationship between river order and FCO₂.

Located at the core of the Guilin Karst World Heritage Site, the Lijiang River Basin serves as a sensitive indicator of carbon cycling in subtropical karst regions². Characterized by numerous tributaries and heterogeneous carbonate rock distributions, its complex environmental factors directly shape the riverine carbon emission characteristics³³. While existing studies have analyzed FCO₂ at typical monitoring transects or along upstream-downstream reaches^34,35, the relationship between Strahler order-based river hierarchy and FCO₂ within the Lijiang River Basin remains poorly understood. Therefore, this study focuses on seasonal variations in two sampling periods, June and December, to investigate FCO₂ dynamics across Strahler-ordered rivers in the basin, as elucidating these CO₂ emission patterns holds critical implications for both heritage conservation and global carbon assessments.

Methods

Study area

Centered around the Lijiang River, the Guilin Karst features a rich tapestry of landscape elements. Distinctive tower karst peaks (fenglin) and cluster peaks (fengcong) are juxtaposed with the clear, meandering waters of the Lijiang River, complemented by rugged, multicolored cliffs and magnificent caves. This ensemble creates a landscape celebrated for its “green mountains, clear waters, extraordinary caves, and beautiful rocks,” embodying exceptional aesthetic value. It represents the quintessence of China’s karst mountain-water scenery and is acclaimed as “the world’s most beautiful and unique karst landscape”². The Lijiang River (24°16’~26°21’N, 109°45’~111°02’E) forms the core catchment of the Guilin Karst World Natural Heritage Site. As the upper reach of the Guijiang River Basin and a significant tributary of the Pearl River, it originates from Mao’er Mountain at an altitude of 2142 m (Fig. 1). The Lijiang River Basin stretches for 164 km and covers a total area of 12,680 km². The basin experiences a subtropical monsoon climate characterized by hot, rainy Junes and cool, dry Decembers. The mean annual precipitation is approximately 2000 mm, with about 80% occurring during the wet season (April to October), indicating pronounced seasonal variability.

Fig. 1: Spatial distribution of sampling sites in the Lijiang River Basin.

Upper left: Geographical location of the Guilin Karst World Natural Heritage Site in China. Lower left: Geographical position of the Lijiang River within the Pearl River Basin. Right: Detailed map of the Lijiang River Basin, showing the distribution of sampling sites (red dots) across different Strahler river orders (1–5) and their association with karst (blue) and non-karst (yellow) lithologies.

Fifty-two sampling sites were established across the basin, encompassing Strahler stream orders 1–5. Sampling sites for orders 1─3 were primarily located in the upper tributaries (e.g., Huangbai River, Chuan River, Lingqu Canal, Xiaorong River), which are numerous in this region. Order 4 sites were situated on larger tributaries (e.g., Darong River, Gantang River, Lipu River), while order 5 sites were positioned along the mainstem in the middle and lower reaches. This fully takes into account the spatial heterogeneity and hydrological connectivity of the basin, ensuring the rational distribution of sampling points and the scientific nature of data collection. The basin topography generally slopes from north to south, dictating the southward flow of the river. The average elevations at the sampling sites for orders 1─5 were 263.45 m, 278.69 m, 222.33 m, 165.60 m, and 126.50 m, respectively (Fig. S1). Sites on orders 1─3 were significantly higher than those on orders 4─5, exhibiting an overall trend of decreasing elevation with increasing river order.

Land cover around orders 1─3 streams was predominantly forest and farmland³⁶, underlain mainly by non-carbonate rocks such as granite and clastic sedimentary rocks. Order 4 rivers were surrounded primarily by farmland and Construction land, and order 5 rivers featured a mix of Construction land, farmland, and forest³⁶, with carbonate rocks (limestone) densely distributed in this zone. Sampling sites on orders 4─5, particularly those in Yangshuo County on the lower order 5 reach, renowned for its superlative karst scenery and thus the most popular section of the Lijiang River, experienced more intensive anthropogenic disturbances, mainly from tourism.

Sampling and analysis

Sampling was conducted from June 15th to July 3rd, 2019, and from December 24th, 2019, to January 5th, 2020, in the mainstem and several tributaries of the five Strahler orders in the Lijiang River Basin, covering a total of 52 sampling sites. Furthermore, most sampling times were concentrated in June and December, so we analyzed June and December as the sampling months to preliminarily indicate the spatiotemporal changes in FCO₂ during summer and winter. At each site, water temperature (T_water), pH, dissolved oxygen (DO), and turbidity (Tb) were measured using YSI ProDSS multi-parameter water quality analyzers (Golden Spring Instruments, Inc.). The instruments were calibrated with pH buffers of 4.00, 7.00, and 10.00, according to the manufacturer’s instructions, prior to measurement. The DO saturation probe was calibrated using water-saturated air. The measurement uncertainties for T_water, pH, DO, and Tb were ±0.1 °C, ±0.01 pH units, ±0.1%, and ±0.03 NTU, respectively. Chlorophyll (Chl-a) concentration was measured using a Trilux fluorometer (Chelsea Technologies Group Ltd., UK), with a resolution of 0.01 μg/L. Air temperature (T_air) and humidity were recorded in the field using the SSN-71USB temperature and humidity meter (formerly Hengtong Technology Co.). Additionally, average wind speed at 2 m above the water surface was measured once per minute during a 30-min gas sampling period using the KANOMAX 6036 handheld anemometer. Flow velocity was measured with a water flow probe, accurate to 0.1 m/s. River width was measured with a laser rangefinder, and water depth was measured onsite.

Water samples were collected at 52 discrete sites using syringes. Each sample was immediately filtered through a 0.45 µm filter membrane and stored in a pre-rinsed 500 mL high-density polyethylene (HDPE) vial for primary ion analysis. For stable carbon isotope (δ¹³C_DIC) analysis of dissolved inorganic carbon (DIC), samples were filtered through a 0.22 µm acetate rayon filter into a 15 mL HDPE bottle. To prevent microbial changes, three drops of saturated HgCl₂ solution were added to each sample. All samples were promptly placed in ice packs upon collection and transported to a refrigerated environment at 4 °C within 12 h. The HCO₃⁻ ion concentration was determined using a Thermo Field ICS-900 ion chromatograph (Dean Company, USA) with an accuracy of 0.01 mg/L. The δ¹³C_DIC was measured using the phosphoric acid method with a MAT253 and Gas Bench continuous flow isotope mass spectrometer, with results reported relative to the V-PDB standard. The analytical error for δ¹³C_DIC was <0.15‰.

In addition, hydrochemical data, including pH, T_water, HCO₃⁻, and the saturation index of calcite ($\text{SIc}=\log (({\text{Ca}}^{2+})({\text{CO}}_{3}^{2-})/{\text{K}}_{\text{c}}$, where K_c is the temperature-dependent equilibrium constant of calcite dissociation) were processed using WATSPEC software³⁷. The pCO₂ was calculated using the CO₂SYS program. Notably, it has been shown that the reliability of pCO₂ calculations from pH, total alkalinity (TA), and temperature is highest in freshwater with pH values ranging from neutral to alkaline and TA exceeding 1000 µmol L⁻¹^38,39. Therefore, in this study, water bodies with TA < 1000 µmol L⁻¹ at the sampling sites were corrected for pCO₂, and the specific correction method is described in the supplementary information.

River classification: Strahler classification method

The Strahler method, an improvement of Horton’s approach, defines river orders using pure graph theory⁴⁰. Strahler’s binary tree sorting method comprises three rules:

(1) Rivers originating directly from river sources are classified as order 1.

(2) When two rivers at the same level converge to form a new river, its order is increased by one compared to the original rivers.

(3) If two rivers of different orders merge, the resulting river adopts the higher order of the original rivers.

These rules are expressed by the following formula:

$${\text{n}}_{\text{d}}=\left\{\,\begin{array}{c}{\text{n}}_{1}+1,{\text{n}}_{1}={\text{n}}_{2}\\ \max \left({\text{n}}_{1},{\text{n}}_{2}\right),{\text{n}}_{1}\ne {\text{n}}_{2}\end{array}\right.$$

(1)

where ${\text{n}}_{\text{d}}$ is the downstream river order, and ${\text{n}}_{1}$ and ${\text{n}}_{2}$ are the orders of the upstream rivers at the confluence. Rivers of Strahler orders 4 and 5 (classified as larger or higher-order rivers) represent the primary channels (major tributaries and mainstem) within the Lijiang River Basin, characterized by a mean width >100 meters. Twenty sampling points were distributed across these higher-order reaches to assess their hydrological and biogeochemical properties. In contrast, headwater streams (orders 1–3, defined as smaller or lower-order rivers) with mean widths <50 meters, were sampled at 32 sites to capture their spatial heterogeneity.

CO₂ degassing flux: Thin boundary layer (TBL) method

The CO₂ degassing fluxes at the water-air interface were calculated using the following equation based on Fick’s law⁴¹:

$${Flux}=K\,({\text{C}}_{\text{water}}-{\text{C}}_{\text{air}})$$

(2)

where the Flux is the CO₂ degassing flux (mmol/(m²·d)), K is the gas transfer velocity (cm/h), and ${\text{C}}_{\text{water}}\,-\,{\text{C}}_{\text{air}}$ is the difference in CO₂ concentration between water and air. We calculate K for freshwater using temperature-dependent Schmidt number (${\text{Sc}}_{\text{T}}$)⁴²:

$$K={K}_{600}\times {({\text{Sc}}_{\text{T}}/600)}^{\text{-}0.5}$$

(3)

with

$${\text{Sc}}_{\text{T}}\text{=}1911.1-118.11\text{T+}3.4527{\text{T}}^{2}-0.04132{\text{T}}^{3}$$

(4)

where T is the in-situ T_water (°C), and K₆₀₀ is the K of CO₂ in freshwater at 20 °C. K values depend on the size of the river²². The mean K₆₀₀ value with channel widths less than 100 m is almost 60% higher than for rivers wider than 100 m, a significant difference. The K₆₀₀ for rivers >100 m wide showed a strong positive correlation with the wind speed (ū₁₀) at 10 m above the river, whereas the K₆₀₀ for rivers <100 m wide showed a significant positive correlation with the river flow velocity, leading to different K₆₀₀ calculations for different river widths. Therefore, based on river hydrodynamic characteristics and referring to previous studies²², we used a river width of 100 m as the threshold to divide sampling points dominated by wind-driven and flow-driven forces. River width increased along the rivers (Fig. 3a), For rivers <100 m, we used the following formula to calculate:

$${K}_{600}=13.82+0.35\omega$$

(5)

K₆₀₀ (cm/h) is the K value at 20 °C. ω is the flow velocity (m/s); the spatiotemporal variation in flow velocity is significant (Fig. 3b).

and rivers >100 m wide are calculated using wind speed related formula²², and wind speed generally increases with the river order (Fig. 3c):

$${K}_{600}=4.46+7.11{\bar{{\rm{\mu }}}}_{10}$$

(6)

${\bar{{\rm{\mu }}}}_{10}$ is the wind speed 10 m above the river, which can be calculated by the following equation:

$${\bar{{\rm{\mu }}}}_{{\rm{z}}}=\left(\frac{{{\rm{\mu }}}^{* }}{k}\right)\mathrm{ln}\left(\frac{z}{{z}_{0}}\right)$$

(7)

where, ${\bar{{\rm{\mu }}}}_{\text{z}}$ is the average wind speed (m/s) at the height of z (m), μ^* is the friction rate (m/s), k is the Von Karman constant (≌0.40), and z₀ is the roughness length (10⁻⁵ m, the middle value of water surface).

To evaluate the reliability of the TBL method in this study, we compared its results against FCO₂ measurements from the floating chamber (FC) method (Fig. S2). The comparison showed that the TBL method exhibited higher stability, and a statistically significant positive correlation was found between the FCO₂ values derived from the two methods. Given the inherently smaller dataset from the FC method, we consequently selected the TBL method as the primary approach for FCO₂ estimation in this study. The detailed comparative analysis is provided in the Supplementary Information.

Results

Control on spatial changes in FCO₂

Our results indicate that FCO₂, pCO₂, and k values all exhibit complex spatiotemporal variations. As shown in Fig. 2, the FCO₂ and pCO₂ were found to show very consistent changes along the river Strahler order. For example, both the FCO₂ and pCO₂ showed a downward trend from order 1 to 5, except for the unusually high values at order 4 in December. Interestingly, an upward trend of both the FCO₂ and pCO₂ occurred as the river Strahler orders, except for the high values of order 1 in June. The fit between FCO₂ and river Strahler order shows a nonlinear relationship (Fig. 2d–f), which differs from the linear trend found in most studies¹⁶, where FCO₂ decreases with increasing river order. In the Lijiang River Basin, FCO₂ deviated from the expected trend in June rivers and December order 4 rivers. In addition, the k values are more consistent in smaller rivers, whereas they fluctuate more significantly in larger rivers. In June, order 4 rivers had lower k values compared to order 5 rivers, while the opposite trend was observed in December.

Fig. 2: Nonlinear dependence of CO₂ dynamics on river order in the Lijiang River.

a–c FCO₂, pCO₂, and k₆₀₀ values in different orders of rivers, where dots represent mean values and vertical lines represent 95% confidence intervals. d–f Nonlinear relationships between river order and FCO₂ as revealed by the nonlinear model across both sampling campaigns in the Lijiang River Basin (after outlier removal). The Akaike Information Criterion (AIC) value of the nonlinear model (1085.84) was significantly lower than that of the linear model (1093.4), indicating a better fit. This superiority was consistent in the seasonal datasets: December (nonlinear AIC = 525.9 vs. linear AIC = 530.78) and June (nonlinear AIC = 461.84 vs. linear AIC = 473.86).

Generally, the FCO₂ values in riverine systems are typically governed by k values and pCO₂ at the water-air interface^7,43. The elevated k values were found to be the key driver of significantly higher FCO₂ in headwater streams compared to larger rivers^20,21. In addition, the marked decline in pCO₂ gradients with increasing river order may also play a critical role in decreased FCO₂ of larger rivers^16,44. To analyze the actual controlling factors of FCO₂, we conducted a variance contribution analysis, which showed that in December, k values and pCO₂ accounted for 7.58% and 91.23% of the variability of FCO₂, respectively, while their contributions shifted to 3.73% and 94.87% in June (Table 1). Regardless of season, pCO₂ exhibited dominant control over FCO₂ variability compared to k values.

Table 1 Multiple linear regression of FCO₂ with pCO₂ and k values in different months

Causes of FCO₂ spatial variation

Riverine CO₂ primarily originates from soil respiration, microbial metabolism, and organic matter decomposition, while being consumed through processes such as carbonate rock weathering and aquatic plant photosynthesis³⁵. Consequently, in June, the observed increase in pCO₂ and FCO₂ along the ascending river Strahler order within the Lijiang River Basin likely stems predominantly from processes including soil respiration, microbial metabolism, and organic matter decomposition. Conversely, in December, the decline in pCO₂ and FCO₂ observed with increasing river order is primarily driven by aquatic plant photosynthesis and carbonate rock weathering. This indicates that the processes governing the spatial distribution of FCO₂ are complex. Nevertheless, by analyzing the parameters indicative of these processes, we can preliminarily infer the key mechanisms governing their variation. Furthermore, pCO₂ was the primary driver of FCO₂ variations in the Lijiang River Basin during both June and December, and its dynamics closely mirrored those of FCO₂. Consequently, subsequent discussions of overall FCO₂ variations will focus primarily on pCO₂ to further elucidate its regulatory mechanisms.

Observational data reveal that T_water increased with the river Strahler orders in both June and December (Fig. 3d). Although elevated T_water theoretically reduces CO₂ solubility in aquatic systems, driving higher CO₂ emissions to the atmosphere⁴⁵, our statistical analysis demonstrated no significant correlation between T_water and pCO₂ (P > 0.05). This finding implies that some other processes play a more important role in driving the observed increase in pCO₂ with increasing river order. DO serves as a key indicator of metabolic processes in aquatic ecosystems³. This study reveals significant spatiotemporal variations in DO concentration (P < 0.01). In June, DO generally decreased with increasing Strahler order, with mean values mostly undersaturated, whereas in December, spatial variability was smaller and mean values largely supersaturated (Fig. 3e). As another crucial parameter, pH tended to increase with stream order (Fig. 3f), further reflecting the response of the aquatic carbonate system to metabolic activity. Photosynthesis typically absorbs CO₂ and releases O₂, thereby elevating DO and pH, while respiration consumes O₂ and releases CO₂, leading to reductions in both DO and pH⁸. pCO₂ exhibited significant negative correlations with both DO and pH in June and December (Fig. 4a, b, P < 0.05), suggesting that aquatic metabolism is likely a key driver of the spatial heterogeneity in pCO₂. This interpretation is further supported by a significant negative correlation between DO deficit (ΔO₂) and CO₂ deficit (ΔCO₂) (Fig. 4c, P < 0.0001).

Fig. 3: Variations in physicochemical and hydrological parameters across different Strahler river orders.

Dots represent mean values, and vertical lines indicate 95% confidence intervals. a, c, d, f, h, k (river width, wind speed, pH, Tb, Chl-a, and SIc) generally increased with higher river orders in both June and December. b, e, i, j, l (water velocity, DO, HCO₃⁻, DIC, and δ¹³C_DIC) exhibited more complex patterns of variation across river orders in both sampling campaigns.

Fig. 4: Linear correlations between parameters in the Lijiang River Basin.

a pCO₂ and DO; b pCO₂ and pH; c DO Deficit (ΔO₂) and CO₂ Deficit (ΔCO₂) in June and December, where Y = −1× represents the ideal state of aquatic metabolic processes, the specific calculation formulas can be found in the supplementary information; d pCO₂ and DIC.

During June, the monsoon season enhances hydrological disturbances (Fig. S3), leading to a marked increase in water turbidity (Fig. 3g). High turbidity reduces light penetration, suppressing photosynthetic efficiency and resulting in predominantly undersaturated DO concentration. Although Chl-a increased with river order (Fig. 3h), indicating biomass accumulation, the predominantly positive ΔO₂ values suggest that enhanced biological activity was likely dominated by respiration. The slope between ΔO₂ and ΔCO₂ was −0.34 in June, greater in magnitude than in December (−0.12), indicating stronger metabolic activity in June. However, the substantial deviation of this slope from the theoretical value of −1 implies that processes other than respiration contributed to CO₂ production. Previous studies have reported that summer rainfall introduces substantial particulate organic carbon (POC) into the Lijiang River Basin⁴⁶ (Fig. S4). Rapid flow in upper reaches and tributaries shortens organic carbon retention time, facilitating its accumulation in downstream segments and providing a significant external carbon input. Coupled with elevated water temperatures that enhance microbial degradation, the observed significant positive correlation between DIC and pCO₂ in June (Fig. 4d, P < 0.05) further suggests that the degradation of organic carbon into DIC supplies an internal carbon source contributing to elevated pCO₂. In summary, both aquatic respiration and the input and degradation of allochthonous organic carbon collectively drive the increase in pCO₂ with river order in June.

In contrast, subtropical rivers in winter maintain relatively higher water temperatures and generally lower turbidity, which favors greater light availability⁴⁷. December observations showed increased Chl-a and predominantly negative ΔO₂, reflecting enhanced phytoplankton photosynthesis. The concurrent increase in dissolved organic carbon (DOC) with river order in December (Fig. S4), together with previous studies suggesting that DOC in the Lijiang River Basin originates mainly from aquatic primary production³⁵, further supports the dominance of photosynthesis. Nevertheless, the slope between ΔO₂ and ΔCO₂ still deviates from the theoretical value, indicating that processes other than photosynthesis also regulate pCO₂. HCO₃⁻, DIC, and SIc generally increased with Strahler order, though localized decreases were observed in order 2 and order 4 rivers (Fig. 3i-k). As the dominant component of DIC, HCO₃⁻ accounted for 87.8% and 93.6% of total DIC in June and December, with mean concentrations of 48.73 ± 40.81 mg/L and 68.10 ± 51.59 mg/L, respectively. It is worth noting that the overall increasing trend in DIC aligns with the expanding distribution of carbonate rocks in the watershed, suggesting that carbonate weathering may be an important source of DIC. The declining trend of pCO₂ with river order in December may be related to the carbon consumption mechanism associated with carbonate weathering, which absorbs CO₂ from the water or atmosphere to generate HCO₃⁻, thereby reducing the potential for CO₂ evasion from the water surface. The specific mechanisms involved will be further discussed in subsequent sections.

In addition, the results revealed anomalously high values of FCO₂ in June for order 1 rivers and in December for order 4 rivers (Fig. 2a), further reflecting the fact that the relationship between river FCO₂ and river order is nonlinear. Elevated FCO₂ may be influenced by higher gas transfer velocity, terrestrial organic carbon input and degradation, respiration by aquatic organisms, and carbonate rock precipitation^3,20,35,48. The contribution of pCO₂ to the variance of FCO₂ in order 1 rivers during June was as high as 99.99% (Table 1), and pCO₂ was significantly positively correlated with FCO₂ (Fig. S5), suggesting that the high pCO₂ in order 1 rivers during June was the main reason for their high FCO₂ values. The study shows that the rapid entry of soil CO₂ into the source stream caused by heavy rainfall in June can quickly accumulate river CO₂ concentrations and form a positive pCO₂ concentration gradient higher than the atmospheric concentration⁴⁹, thereby causing an increase in FCO₂. The sampling of order 1 rivers in June coincided with heavy rainfall, so it is speculated that the rapid accumulation of CO₂ from the riverbank soil into the river may have caused the increase in FCO₂. The variance contribution to FCO₂ showed that the k values of order 4 rivers in December accounted for 61.82%, and FCO₂ showed a significant positive correlation with k values (Fig. S5), indicating that higher gas transfer velocity due to high wind speed is the main reason for the anomalous elevation of FCO₂ in order 4 rivers in December.

In summary, our preliminary findings indicate that in the Lijiang River Basin, metabolic processes, terrestrial carbon input and degradation, carbonate dissolution and precipitation collectively drive the variations in pCO₂, resulting in contrasting patterns of FCO₂ changes with river order across different seasonal sampling periods. Furthermore, the influence of k values, affected by wind speed at specific river orders, should not be overlooked. In conclusion, the relationship between FCO₂ and river order in the basin more accurately exhibits nonlinear characteristics, rather than following a simplistic monotonic pattern of decrease with increasing river order.

Sources and variations of riverine δ ¹³C_DIC

The riverine DIC is mainly derived from the following processes: CO₂ exchange with the atmosphere, soil CO₂ inflow through groundwater, biological respiration in rivers, and weathering of carbonate rocks^50,51. Each source has a unique isotopic signal, which causes the δ¹³C_DIC value in rivers to vary greatly. Therefore, δ¹³C_DIC can be used to analyze the sources and dynamic changes of DIC in rivers⁵². Since CO₂ concentrations in soil are typically much higher than in the atmosphere, the CO₂ consumed during rock weathering primarily comes from soil respiration, with the contribution from atmospheric CO₂ (δ¹³C ≈ − 8‰) being negligible⁵³. In the Lijiang River Basin, soil CO₂ mainly results from the respiration of C3 plants, with δ¹³C values ranging from −29.35‰ to −18.26‰ and averaging −24.26‰⁵⁴. The widespread marine sedimentary carbonates in the region have δ¹³C values close to 0‰⁵⁵. According to the classic carbonate weathering model, when carbonic acid (H₂CO₃, formed by the dissolution of soil CO₂ in water) reacts with carbonate rocks, the stoichiometry of the reaction indicates that for every two HCO₃⁻ ions produced, one carbon atom comes from soil CO₂ and the other from the carbonate rock⁵⁶. Therefore, the theoretical δ¹³C value of the resulting DIC should be approximately −12‰. Observations of karst groundwater in our study area confirm that δ¹³C_DIC values mostly range from −15.03‰ to −11.53‰, generally aligning with the expected carbonate dissolution signature⁵⁷. And in surface waters of the Lijiang River Basin, δ¹³C_DIC values range from −13.75‰ to −3.38%, with an average of −8.62%, and all values are above −12‰ (Fig. 3l), showing a distinct positive deviation. This deviation suggests that the proportion of carbon from carbonate rocks in the DIC is much higher than the 50% predicted by the classic model. Previous quantitative studies support this conclusion, with estimates based on hydrochemical and isotope mixing models indicating that carbonate weathering contributes 87–95% of the DIC^56,58, overwhelmingly dominating its source. These data confirm that carbonate weathering is the primary source of DIC in this basin, and its high δ¹³C signal (≈0‰) raises the δ¹³C_DIC value, effectively diluting the negative isotope signal from soil CO₂ (≈−24‰). Additionally, other biogeochemical processes, such as organic matter degradation, respiration, and calcite precipitation, lower δ¹³C_DIC values, while photosynthesis, CO₂ outgassing, and carbonate dissolution raise them⁵⁰, but the net effect of these processes does not alter the dominant carbonate-derived isotopic signature of the DIC.

As shown in Fig. 5a, DIC and δ¹³C_DIC exhibited a significant negative correlation (r = −0.45, P < 0.01) in June rivers, suggesting that a single process may have driven concurrent DIC enrichment and a decline in δ¹³C_DIC values. Typically, aquatic plant respiration uptake of O₂ and preferential release of ¹²C lead to increased DIC concentrations and decreased δ¹³C_DIC values⁵⁹. Previous studies on the Lijiang River basin have found a significant correlation between DOC and DIC⁴⁶ (P < 0.05, Fig. S3), indicating that DIC released by the decomposition of organic matter in rivers has an impact on the DIC pool. Furthermore, a positive correlation between DIC and Chl-a in June may imply that increased algal biomass enhanced respiratory substrate availability for aquatic organisms (Fig. 5c). Concurrently, the negative correlation between DIC and DO, along with widespread DO undersaturation, reflects enhanced respiratory oxygen consumption. Additionally, DIC correlated positively with both Tb and T_water in June. Elevated Tb suggests that monsoon rainfall intensified the input of terrestrial particulate organic carbon, which is known to be higher in June and predominantly allochthonous in this basin⁴⁶. Increased T_water further stimulates microbial respiration and accelerates organic carbon degradation⁶⁰. The synergistic effect of these factors may drive the increase in DIC concentration and significantly reduce the δ¹³C_DIC value through the release of low δ¹³C respiratory CO₂. Although carbonate dissolution contributes to DIC accumulation, a significant negative correlation between SIc and δ¹³C_DIC values (Fig. 5c), along with the decrease in δ¹³C_DIC values with increasing river order, may suggest that the changes in pCO₂ and DIC during June are primarily driven by respiration and organic carbon degradation, rather than by carbonate dissolution processes.

Fig. 5: Relationships and drivers of DIC across seasons.

a, b Linear fit of δ¹³C_DIC to DIC in June and December, and c, d a heatmap of the correlation between DIC and each parameter in June and December.

On the contrary, the increase in DIC and δ¹³C_DIC values during December is influenced by various processes (Fig. 5b, P > 0.05). In December, DOC increased with river order (Fig. S3), and it is known that DOC mainly originates from the primary productivity of aquatic organisms⁴⁶, indicating that photosynthesis gradually intensified as river order increased. The Chl-a increased with river order and was positively correlated with DIC and δ¹³C_DIC values (Fig. 5d), reflecting enhanced autotrophic activity and the preferential assimilation of ¹²C by algae photosynthesis, leading to the enrichment of ¹³C in residual DIC and a significant reduction in water CO₂ concentration, which may contribute to the increase in δ¹³C_DIC. In addition, although DO concentrations fluctuate greatly, their supersaturation may also indirectly reflect enhanced photosynthesis, indicating that δ¹³C_DIC values may be affected by photosynthesis and vary with river order. At the same time, the increase in SIc with increasing river order and its strong correlation with DIC (r = 0.85, P < 0.001) indicates enhanced carbonate weathering, which is consistent with the background of higher-order rivers mainly flowing through carbonate rock areas. Carbonate rocks typically have a relatively heavy carbon isotope composition. As such, enhanced dissolution of carbonate rocks (CaCO₃) contributes proportionally more to DIC pools via reactions like CaCO₃ + CO₂ + H₂O → Ca²⁺ + 2HCO₃⁻, thereby elevating the bulk δ¹³C of DIC. Aquatic biomes utilize DIC derived from carbonate rock weathering to convert it into OC⁵⁸. Dissolved CO₂ in the water body is continuously utilized to replenish DIC, leading to a decrease in dissolved CO₂ concentration, which may also contribute to the reduction in FCO₂ in higher-order rivers. Thus, compared to lower-order rivers flowing through non-karst regions, higher-order rivers are influenced by carbonate rock weathering, resulting in higher DIC content and greater CO₂ consumption.

Overall, we tentatively speculate that the enrichment of DIC and the decline in δ¹³C_DIC in June may be influenced by aquatic respiration and organic carbon mineralization, while in December, although carbonate weathering increases DIC stocks and δ¹³C_DIC values, the accompanying CO₂ consumption synergizes with photosynthetic CO₂ fixation, which may also jointly drive the decline in FCO₂ in higher-order rivers.

Discussion

As a core component of the “Guilin Karst” UNESCO World Heritage Site, the Lijiang River Basin showcases the globally representative tower-shaped karst landscape, presenting typical pinnacle formations in a humid tropical-subtropical environment². It holds irreplaceable geological significance, exceptional aesthetic value, and crucial ecological functions. Preserving the integrity of this basin is vital to ensuring the long-term sustainability of the heritage site. On a global scale, CO₂ emissions from rivers generally exhibit significant spatiotemporal heterogeneity⁷. The unique geology of karst river basins, such as the Lijiang River Basin, introduces greater complexity into the air-water CO₂ exchange process²⁹. Therefore, systematically analyzing the spatiotemporal variation characteristics of FCO₂ in the Lijiang River Basin and its driving mechanisms not only helps reveal the coupling relationship between geological and ecological processes in the karst carbon cycle but also provides important scientific evidence for assessing the potential impacts of climate change, hydrological fluctuations, and human activities on the carbon cycle of this World Heritage site.

Our study found that, unlike previous studies, which generally pointed to a linear decrease in FCO₂ with increasing river Strahler order^16,17, in the Lijiang River Basin, there is a nonlinear relationship between FCO₂ and river order. During June, FCO₂ increases with the river order, which may primarily be influenced by respiration and organic carbon degradation. In contrast, in December, FCO₂ shows a declining trend with increasing river order, which we preliminarily attribute to the combined effects of photosynthesis and carbonate dissolution. Additionally, some order rivers in the basin show seasonal variations that deviate from expected values due to increased gas transfer velocities driven by wind speed and potential soil CO₂ input. As a result, the relationship between river order and FCO₂ in a single basin is typically nonlinear and is influenced by wind speed, terrestrial carbon input and degradation, internal metabolic processes, and geochemical factors. More notably, the higher k values and pCO₂ gradient differences observed in lower-order rivers are not the only determining factor for the spatial variability of FCO₂ in the basin^32,43. As the river order increases, more significant terrestrial carbon input and decomposition, enhanced biogeochemical processes, wind speed, and biological factors jointly lead to increased variability in k values and pCO₂, which may cause the FCO₂ in the basin to exhibit more complex trends with changes in river order.

In order to further validate the differences in FCO₂ of different order rivers, we comparatively analyzed the differences in CO₂ emissions between lower and higher-order streams in the Lijiang and the Pearl River Basins. As shown in Table 2, in the Lijiang River Basin, the lower-order streams (Strahler orders 1–3) accounted for 39% and 37% of the total CO₂ emissions during June and December, respectively. While December CO₂ emissions exceeded their areal contribution (28% of the total water surface area), June CO₂ emissions approximately match their area proportion (38%). Throughout the year, lower-order streams accounted for 34% of the total water surface area (Fig. 6) but contributed only 38% of the total CO₂ fluxes. Thus, CO₂ emissions from the Lijiang River Basin, while also exhibiting some disproportionate contribution, are in marked contrast to the Pearl River Basin. From Table 2, lower-order streams in the Pearl River Basin (Strahler orders 0–2) account for only 31% of the total water surface area but contribute 75% of the total CO₂ flux¹⁶. These comparative results demonstrate that watershed-scale CO₂ emissions pronounced nonlinear scaling with stream order and are not constant due to significant spatiotemporal heterogeneity in FCO₂ at different order rivers.

Fig. 6: Water surface area distribution and its scaling with stream order.

a Water surface area in each Strahler order in the Lijiang River Basin in June and December, and exponential relationship between river Strahler order and b total river length, c river width in June, and d river width in December.

Table 2 Comparison of FCO₂ between the Lijiang River Basin and Pearl River Basin

Additionally, the variance analysis (Table 3) reveals that FCO₂ is a key factor driving the variation in the total CO₂ flux in the Lijiang River Basin, with its influence particularly pronounced in June for lower-order rivers. The contribution rate of FCO₂ (40.41%) is significantly higher than that of the corresponding water surface area (30.99%), indicating that CO₂ degassing intensity dominates the spatial variation of total flux during this period. Notably, this phenomenon is also partly observed in higher-order rivers (Strahler orders 4–5) during December, where the contribution rate of FCO₂ (41.61%) is nearly equal to that of the water surface area (42.83%). However, the water surface area of higher-order rivers in June and lower-order rivers in December contributes significantly more to the total CO₂ flux (44.11%/67.51%) than FCO₂ (35.16%/15.39%), highlighting the important regulatory role of water surface area in CO₂ emissions throughout the Lijiang River Basin. This results in a stark contrast with the carbon emission contribution pattern of lower-order rivers in the Pearl River Basin. Specifically, lower-order rivers in the Pearl River Basin exhibit an asymmetric relationship between carbon emissions and area (i.e., “disproportionate contribution”), whereas this study finds that the carbon emission contribution ratio of lower-order rivers in the Lijiang River Basin (34% of water surface area corresponding to 38% of total CO₂ flux) is more evenly distributed, with only a slight deviation. In the Lijiang River Basin, lower-order rivers contribute less to total CO₂ emissions (39% in June, 37% in December) due to the synergistic control of FCO₂ intensity and water surface area. During June, their combination of lower FCO₂ and limited areal extent constrains emissions, whereas higher-order rivers dominate through elevated FCO₂ and extensive surface coverage. In December, despite higher FCO₂ in lower-order rivers, their minimal surface area restricts total output; higher-order rivers, conversely, utilize substantial areal dominance to sustain high emission contributions even with reduced per-unit-area FCO₂. This pattern establishes higher-order rivers as the basin’s primary carbon emission sources across both seasons.

Table 3 Multiple linear regression of total CO₂ flux with FCO₂ and water surface area in different months in the Lijiang River Basin

In conclusion, this study provides preliminary evidence of a nonlinear relationship between FCO₂ and the Strahler stream order in the Lijiang River Basin, deepening our understanding of the carbon emission processes in karst systems and laying a scientific foundation for integrating geochemical knowledge into landscape conservation strategies. Based on discrete sampling data from June (summer) and December (winter), we obtained the following main findings:

• (1) Spatiotemporal heterogeneity of FCO₂: Observations in June showed that FCO₂ increased with river Strahler order, likely related to respiration and organic carbon degradation. In contrast, observations in December showed that FCO₂ decreased with increasing river order, primarily influenced by photosynthesis and carbonate weathering.

• (2) Abnormal FCO₂ behavior in specific river orders: In certain Strahler stream orders, increased wind speed (enhancing gas transfer velocity) combined with terrestrial organic carbon input led to FCO₂ deviating from the expected trend.

• (3) Shift in Contribution Pattern: Contrary to the traditional “headwater dominance” paradigm, the combined influence of FCO₂ magnitude and water surface area resulted in a relatively reduced contribution of lower-order streams to the total basin-scale CO₂ flux. These findings challenge existing hypotheses regarding fluvial carbon flux controls and underscore the necessity of multi-basin studies to address scale-dependent uncertainties in carbon budgets.

Furthermore, the analysis of FCO₂ dynamics is mainly based on seasonal samples taken in June and December. While it effectively captures the typical features of summer and winter, higher-resolution time-series data would help further reveal the details of its diurnal dynamics and key driving mechanisms. Additionally, the nonlinear relationship observed between FCO₂ and river order in the Lijiang karst World Heritage site reflects the unique combination of biogeochemical processes in the region. The model established under this specific context needs to be validated in other hydrological and geological settings when applied to other watersheds. Therefore, to address these limitations, future research could integrate multi-scale, multi-basin observational data to test the universality and variability of such relationships across different ecosystems.