The Yellow River rises in the Bayankara Mountains of Qinghai Province, China, and runs through nine provinces before emptying into the Bohai Sea. These provinces are Qinghai, Sichuan, Gansu, Ningxia, Inner Mongolia, Shanxi, Shaanxi, Henan, and Shandong. It encompasses a basin area of 795,000 km² and is 5,464 kilometers long overall. (Figure 2). Ensuring the reasonable and sustainable utilization of these lands is crucial for continued regional development.

CO₂ emission sources in the Yellow River Basin (YRB) can be classified into 3 main groups. The first group is industrial activities. Heavy industries such as cement production and steel manufacturing significantly impact regional CO₂ emissions because of their high emission characteristics during the industrial production process due to the combustion of fossil fuel. The secondly group is agricultural practices, which contribute to the emissions of greenhouse gases, including both CO and CO₂. Activities such as fertilizer application, tillage, and rice cultivation emit these gases through microbial processes. The third group is municipal solid waste (MSW) treatment. Landfilling and incineration add to CO₂ emissions. Organic waste decomposition in landfills generates methane, whereas incineration releases CO₂ and other harmful gases. Additionally, livestock farming, particularly with ruminant animals such as cows and goats, is a significant source of CO₂ emissions in the YRB.

CO₂ absorption in the Yellow River Basin (YRB) occurs primarily in natural ecosystems and urban green spaces. Forests and grasslands serve as major terrestrial carbon sinks, actively converting atmospheric CO₂ into organic matter through photosynthesis and storing it in vegetation and soil. Forest ecosystems, in particular, possess significant carbon storage capacity, with tree canopies and roots contributing to biomass accumulation. The decomposition of fallen leaves and litter further promotes long-term carbon fixation in the soil. Wetlands and reservoirs in the YRB also play crucial roles in the carbon cycle. These water bodies effectively store carbon through the photosynthesis of aquatic plants and the decomposition of dead plant tissues. The anaerobic environment of wetlands slows the decomposition rate of organic matter, facilitating long-term stable carbon storage. Compared with natural ecosystems, urban green spaces, including city parks, street greenbelts, community gardens, and roof gardens, contribute to CO₂ absorption in cities, albeit on a smaller scale. Soil, one of the largest active carbon pools on Earth, has significant carbon storage potential that can be enhanced through sustainable land management practices such as no-tillage, organic agriculture, rotation and intercropping systems, and the application of organic fertilizers.

To address the multiple challenges facing the YRB, including water resource management, ecological protection, and land use, concerted efforts from the government and all stakeholders are essential. The formulation of scientific, thoughtful, and practical policies and measures is crucial to promoting sustainable development in the basin, ensuring economic prosperity, ecological balance, and social progress.

Taking 2013–2022 as an example, the data for the nine provinces in the Yellow River Basin were collected from the IPCC2006 report [Publications - IPCC-TFI (iges.or.jp)], China Statistical Yearbook (stats.gov.cn), China Environmental Statistical Yearbook (nbsti.net), China Energy Statistical Yearbook (ctbu.edu.cn), and China Rural Statistical Yearbook (ctbu.edu.cn). The missing data were treated by interpolation, and these data were checked, examined and finally developed into a socioeconomic database for further analyses.

To maintain data integrity and ensure analytical accuracy, we employed multiple interpolation methods to handle anomalies in the data, including missing values and negative numbers. In this study, five distinct interpolation methods were utilized: linear interpolation, nearest-neighbor interpolation, median interpolation, polynomial interpolation, and spline interpolation. Comparing the efficacy of different approaches and choosing the best strategy based on the study’s data characteristics was the aim.

Linear interpolation is a straightforward and commonly used method that assumes a linear relationship between adjacent data points. This method constructs a linear function based on known data points and calculates the interpolated value for anomalies by leveraging the linear relationship between neighboring normal data points. Nearest-neighbor interpolation replaces anomalies with the closest non-anomalous value. In the implementation, we iterated through all anomalies, identified the nearest normal data point, and assigned its value to the anomaly’s position. Median interpolation involves calculating the median of non-anomalous values within a defined window around the anomaly and using this median as the interpolated value. Specifically, for each anomaly, a window of a certain range before and after the anomaly was determined, non-anomalous values within the window were extracted, and their median was computed and used to replace the anomaly. Polynomial interpolation approximates the data’s trend by fitting a polynomial function. We used the “polyfit” function from the “numpy” library to fit a cubic polynomial, obtained the polynomial coefficients, and then created the polynomial function using the “poly1d” function. This function was subsequently applied to interpolate the anomalies. Spline interpolation employs cubic spline functions, which ensure smoothness while effectively capturing local features of the data. We utilized the “CubicSpline” function from the “scipy” library, with boundary conditions set to “natural,” to perform spline interpolation.

We evaluated each strategy using MSE and MAE in order to determine the best interpolation technique. The average squared discrepancy between expected and actual values is measured by MSE. while MAE represents the average absolute difference. Lower error values indicate better interpolation performance. By comparing the evaluation metrics of different interpolation methods, we considered factors such as error magnitude, data characteristics, and research requirements. Ultimately, we chose different interpolation methods for different datasets, aiming to minimize error values. This approach ensures data accuracy while better reflecting the inherent patterns in the data, providing a solid basis for further research and model development.

Innovative strategies are desperately needed to support both the YRB’s ecological conservation and high-quality interregional growth. Existing ecological compensation mechanisms often inadequately address the regional disparities in carbon emissions and absorption capacities. This study proposes a horizontal carbon ecological compensation mechanism aimed at promoting regional collaborative governance in the YRB by internalizing the externalities of ecological services. The constructed horizontal carbon ecological compensation mechanism in the YRB aims to strengthen basin governance. To improve basin governance, the YRB has implemented a horizontal carbon ecological compensation scheme. It treats carbon emission rights as a limited resource while recognizing the CO₂ absorption capacity of provinces along the Yellow River Basin as a source of revenue. By internalizing the externalities of ecological basin services, this mechanism utilizes interprovincial transfer payments to promote high-quality regional development. It promotes voluntary trade for horizontal carbon ecological compensation amongst YRB provinces. The supply subject is one of the main parties taking part in the YRB’s horizontal carbon ecological compensation system. This mechanism facilitates voluntary carbon emission rights trading among provinces in the YRB. Machine learning is applied to simulate these transactions and predict net carbon emissions across provinces, evaluating the horizontal carbon ecological compensating mechanism’s efficacy.

The carbon emissions, carbon absorption, and net carbon emissions of nine provinces in various years were derived by adding matching data into the model. Table 4 displays the particular outcomes.

For provinces with a carbon surplus, “protection” is chosen as a strategy when the benefits of ecological protection outweigh the associated costs. However, in practice, the benefits often do not outweigh the costs incurred. To prevent carbon surplus and deficit provinces from falling into a “prisoner’s dilemma” scenario where neither protection nor compensation is chosen, the central government acts as an impartial third party. It implements reward and punishment policies to supervise and incentivize appropriate actions. The parameters of the central government’s reward and punishment mechanism depend on the costs and benefits of carbon surplus provinces engaging in ecological protection, as well as the compensation required by carbon deficit provinces. The costs and benefits involved in calculating compensation and the participation of carbon surplus provinces in ecological protection are detailed in Table 5. The scope of rewards and punishments for the supervision mechanism established by the central government is shown in Table 6.

The output results of the supply forecasting model and the demand forecasting model are shown in Table 7 (Figure 6).

The sensitivity analysis was conducted on six key features—demand elasticity, supply elasticity, carbon price, trade volume, and demand quantity—to evaluate their impact on supply quantity. The results are visualized in Figure 7 that illustrates the average predicted supply quantity and the standard deviation of predictions corresponding to different scaled values of demand elasticity. For supply elasticity, as the scaled value increases from 0.0000 to 0.3333, the average predicted supply quantity remains constant at 6.7863 × 10 11 , indicating no significant impact of supply elasticity changes on supply quantity predictions within this range. However, when the scaled supply elasticity reaches 0.4444, the average predicted value drops to 6.7285 × 10 11 and remains stable in the range of 0.4444–0.6667. It then continues to decline, reaching 6.3952 × 10 11 at 0.8889 and further dropping to 6.3569 × 10 11 at 1.0000. Overall, there is a trend of decreasing average predicted supply quantity with increasing supply elasticity. Supply elasticity measures the responsiveness of supply quantity to changes in factors like price. The decline in average predicted values with higher supply elasticity suggests that as supply becomes more sensitive to price changes, the market supply quantity decreases. This could be because, under high supply elasticity, producers are more likely to adjust production in response to market uncertainties, potentially reducing supply.

Regarding carbon price, as the scaled price increases from 0.0000, the average predicted supply quantity initially rises and then stabilizes with slight fluctuations. From 0.0000 to 0.3333, the average predicted value increases from 6.4351 × 10 11 to 6.6863 × 10 11 , indicating a significant stimulative effect of price increases on supply quantity within this range. Between 0.3333 and 0.4444, the average predicted value remains unchanged, suggesting that at this price level, the net carbon emissions of carbon-surplus provinces have reached a certain scale, and further price increases do not immediately lead to additional supply. As the price continues to rise, the average predicted value shows minor increases and fluctuations, reaching 6.7108 × 10 11 at a scaled price of 1.0000.

The sensitivity analysis for marginal revenue shows the average predicted supply quantity and its standard deviation corresponding to different scaled marginal revenue values. As the scaled marginal revenue increases from 0.0000, the average predicted supply quantity generally declines, starting from 6.6222 × 10 11 and gradually decreasing to 6.5750 × 10 11 . The average predicted value remains stable in the ranges of 0.3333–0.4444 and 0.7778 to 1.0000. The decrease in average predicted values with increasing marginal revenue suggests that, under the given market conditions, carbon-surplus provinces may adjust their environmental measures as marginal revenue rises.

For trade volume, as the scaled value increases from 0, the average predicted demand quantity shows an overall upward trend. Similarly, for demand quantity, as the scaled value increases from 0.0000, the average predicted supply quantity initially rises and then stabilizes. At lower scaled demand values (0.0000–0.3333), the average predicted value increases rapidly from 6.3874 × 10 11 to 6.6622 × 10 11 , indicating a strong pull effect of demand increases on supply quantity. Beyond 0.3333, the average predicted value continues to rise but at a diminishing rate. In the range of 0.7778–0.8889, the average predicted value remains constant at 6.7509 × 10 11 , and it slightly decreases to 6.7470 × 10 11 at 1.0000. This implies that once demand reaches a certain level, further increases in supply quantity face.

Another sensitivity analysis was conducted on the six characteristic values. The results of the sensitivity analysis of demand elasticity, supply elasticity, carbon price, trading volume, and supply quantity with respect to demand quantity are as follows. The Figure 8 shows the average predicted value of the supply quantity and the standard deviation of the predicted value corresponding to different scaled demand elasticity values.

For the sensitivity analysis of demand elasticity, when the scaling value of demand elasticity starts to increase from 0, the average predicted demand quantity generally shows a trend of first decreasing and then increasing. When the scaling value ranges from 0 to approximately 0.4444, the average predicted demand quantity gradually decreases, from 6.5201197 × 10¹¹ to 6.3259989 × 10¹¹. In this range, the increase in demand elasticity makes the market demand more sensitive to factors such as price. Carbon - deficit provinces may significantly adjust their purchase volume due to small price changes, resulting in a decrease in the predicted value of the overall demand quantity. When the scaling value of demand elasticity exceeds 0.4444, the average predicted demand quantity begins to rise again, indicating that at a higher level of demand elasticity, some special situations occur in the market, so that even though demand is sensitive to price, the overall demand quantity still increases. Demand elasticity reflects the sensitivity of the demand quantity to changes in factors such as price. In the stage of low demand elasticity, carbon - deficit provinces are not very sensitive to price changes, and the government can increase the income of carbon - surplus provinces by appropriately adjusting the price. In the stage of high demand elasticity, small price changes may lead to large fluctuations in the demand quantity, so the government needs to be more cautious in formulating price strategies.

When the scaling value of supply elasticity is between 0 and 0.3333, the average predicted demand quantity remains unchanged. Starting from 0.4444, the average predicted demand quantity generally shows a downward trend, gradually decreasing from 6.4002166 × 10¹¹ to 6.3259989 × 10¹¹. This indicates that when the supply elasticity exceeds a certain threshold, the supply becomes more sensitive to factors such as price, which may lead to instability in the commodity supply in the market, thus affecting the demand expectations of carbon - deficit provinces and causing the predicted demand quantity to decline.

As the price scaling value gradually increases from 0, the average predicted demand quantity generally shows an upward trend. When the price scaling value is relatively low (around 0–0.2222), the change in the average predicted demand quantity is relatively gentle. When the price scaling value exceeds 0.2222, the increase in the average predicted demand quantity becomes more significant, reaching 6.6575625 × 10¹¹ when the price scaling value is 0.9999. It is possible that carbon - deficit provinces regard the price increase as a signal of increased commodity scarcity, thus increasing their willingness to purchase.

When the marginal revenue scaling value increases from 0, the average predicted demand quantity generally shows a downward trend. When the marginal revenue scaling value is 0, the average predicted demand quantity is relatively high in some cases. As the marginal revenue scaling value increases to 0.1111, the average predicted demand quantity drops to 6.3401310 × 10¹¹, and then continues to decline and remains basically stable in the range of 0.3333–1.0. The extra money made by each extra unit of output is represented by the marginal revenue. When there is little marginal income, carbon - surplus provinces may adopt a low - price strategy to expand sales volume, thus stimulating market demand and making the predicted demand quantity relatively high. As the marginal revenue increases, carbon - surplus provinces may raise prices to obtain higher profits, which will suppress the purchasing willingness of carbon - deficit provinces and lead to a decrease in the demand quantity. When the marginal revenue reaches a certain level, the price and output strategies are relatively stable, so the predicted value of the demand quantity also tends to be stable.

Carbon emissions in the Yellow River Basin gradually increased from 2013 to 2022 (Figure 9), which is consistent with the findings of Zhao (Zhao et al., 2022). Concurrently, the increase in carbon absorption has helped mitigate net carbon emissions. Factors such as economic and industrial development, the energy structure, policy interventions, technological advancements and natural conditions have collectively influenced the overall carbon emissions and absorption dynamics in the YRB. In the upstream areas, carbon absorption significantly outweighs emissions, resulting in negative net carbon emissions. However, the middle reaches experienced notable increases in carbon emissions, leading to a continued increase in net carbon emissions. Conversely, the downstream region achieved substantial reductions in carbon emissions through industrial adjustments and technological advancements, which is consistent with previous research by Meng (Meng et al., 2023).

According to recent research, effective oversight by the central government is essential for establishing ecological compensation systems in river basins (Wang Q. et al., 2022). However, the absence of sufficient checks and incentives from local governments poses a significant challenge to developing such mechanisms across various river basins in China (Jing and Zhang, 2021). As discussed in Section 3.2, the current conditions do not support the evolution of society’s desired optimal strategy into a stable approach within the game system, highlighting the critical need for implementing a reward and punishment mechanism. Further exploration in Section 3.2 revealed that the parameter range for introducing this mechanism by the central government hinges on the costs and benefits associated with carbon surplus provinces engaging in carbon ecological protection, as well as the compensation provided to carbon deficit provinces.

Currently, the research on ecological compensation predominantly focuses on theoretical policies, compensation methods, and the necessity of compensation (Jing et al., 2021). Specific discussions on the operational mechanisms of ecological compensation are limited. Building upon previous research, this study explores the development of a horizontal carbon ecological compensation mechanism in the YRB.

The horizontal carbon ecological compensation mechanism in the YRB promotes carbon emission reduction through market-based approaches, primarily voluntary trading. At its core, the scheme facilitates the emission rights of CO₂ trading, enabling carbon-deficit provinces to collaborate with carbon-surplus provinces. This partnership involves investing in emission reduction projects funded by compensation mechanisms aimed at achieving a balance in carbon emissions. The YRB Carbon Reduction Promotion Center, established by the Ministry of Ecology and Environment, oversees the establishment of registration and trading institutions and related systems to ensure the standardization and transparency of trading (Figure 10). The national carbon emission trading market operates under established laws and regulations, compensation scope, trading management system, monitoring, reporting, and verification (MRV) system, and regulatory mechanism. Implementation of the MRV system guarantees the authenticity of the emissions data and the trading accuracy, whereas regulatory mechanisms include supervision, management, and legal responsibilities to uphold market integrity and health. The total amount of carbon emission trading in the YRB is determined on the basis of the net carbon emissions of the provinces with a carbon surplus and is managed through the national carbon emission trading system, which supports various trading methods. The participants include the suppliers, demanders, regulators, technical support system operators and trading platform operators. The carbon surplus provinces serve as the suppliers, whereas the carbon deficit provinces act as the demanders. The central government functions as the regulatory body, ensuring fairness in the privatization process of public property rights. Technical support systems and trading platforms record transactions and provide settlement services. The carbon trading process involves identifying supply and demand parties, forming a “carbon ledger,” and trading emission reduction credits on the basis of projects, products, or public low-carbon behaviour. Project development must adhere to the nationally standardized voluntary greenhouse gas emission reduction methodology and undergo rigorous procedures, including filing, evaluation, monitoring, verification and certification. Low-carbon products are required to undergo carbon footprint calculations and public disclosure, whereas public low-carbon behaviour is quantified through an app and recorded in a personal “carbon ledger.” Third-party certification verifies emission reductions to ensure methodological applicability and calculation accuracy. The main functions of the trading platform include account opening review, consultation, market promotion, and other services to supervise trading behaviour and prevent risks. The central government has established a reward and punishment mechanism to promote the adoption of optimal strategies, along with a regulatory information sharing and law enforcement cooperation mechanism with relevant departments. The settlement bank provides services such as fund settlements, financial products, carbon trading settlements, financial advice and support within the system to ensure smooth and secure fund flow. It also offers financial solutions for projects and assists in planning capital operations and management strategies. Through these measures, the horizontal carbon ecological compensation mechanism in the YRB aims to effectively control carbon emissions, promote rational resource allocation, and achieve sustainable development of the ecological environment.

This study mainly focuses on the carbon ecological compensation mechanism Different carbon sink generation pathways have varying effects on other ecosystem functions such as water quality and biodiversity.

Forests are important carbon sinks, and their carbon storage can be increased through afforestation and forest management. However, although monoculture plantations can rapidly increase carbon sinks, they may reduce biodiversity as they suppress the growth of understory vegetation, thus reducing food sources and habitats for insects and birds. In contrast, broad - leaved mixed forests can provide complex habitat structures, promoting the development of biodiversity. In terms of water quality, healthy forests can reduce soil erosion, purify rainwater, and lower the pollutant content in water bodies. Nevertheless, large - scale deforestation or unreasonable afforestation can damage the soil structure, exacerbate soil erosion, and affect water quality.

Wetlands are also significant carbon sinks, with their unique environments capable of storing large amounts of organic carbon. Wetlands serve as habitats for numerous rare animals and plants. Protecting and restoring wetlands can increase biodiversity. For example, coastal wetlands are crucial for the survival and migration of migratory birds. Moreover, wetlands have a powerful water purification function. Wetland plants can absorb and transform nutrients in water bodies, and the soil and microorganisms can decompose and remove pollutants. Constructed wetlands are widely used in sewage treatment.

In farmland, reasonable management measures such as no - tillage, straw returning, and the application of organic fertilizers can increase soil carbon storage. Increasing farmland carbon sinks can improve soil structure, enhance fertility, and water and fertilizer retention capacity. Straw returning can increase soil organic matter, improve aeration and water permeability. Reasonable management can also provide a suitable environment for farmland organisms, increasing biodiversity. For instance, reserving natural habitats around farmland can provide food and habitats for insects, birds, and small mammals.

The ocean is the largest carbon reservoir on Earth, and its carbon sinks are mainly achieved through the photosynthesis of phytoplankton and the calcification of marine organisms. The increase in ocean carbon sinks helps to regulate the global climate and slow down the rise of atmospheric carbon dioxide concentration. Marine biodiversity is closely related to the carbon sink process. Phytoplankton are the basis of the marine food chain. Protecting the marine environment and promoting the increase of carbon sinks are beneficial for maintaining biodiversity. However, overfishing and pollution can disrupt the ecological balance, affecting carbon sink functions and biodiversity.

Grasslands can increase carbon sinks through reasonable grazing management, protection, and restoration. The roots of grassland vegetation can fix the soil and prevent erosion. Reasonable grazing can promote vegetation growth and enhance the soil’s anti - erosion ability. Grasslands provide habitats for many animals and plants, and reasonable management helps to maintain biodiversity. Overgrazing can lead to grassland degradation and a decline in biodiversity.

Although desert ecosystems have sparse vegetation, they also have certain carbon sink functions, which are realized through the photosynthesis of desert plants and soil carbon fixation. The growth of desert plants can improve soil quality, fix sand, and reduce wind - sand erosion. They also provide habitats for unique biological communities. However, human activities such as over - reclamation and over - exploitation of water resources can damage desert ecosystems, affecting carbon sink functions and biodiversity.

In conclusion, when implementing the carbon ecological compensation mechanism, the impacts of different carbon sink pathways on other ecosystem functions should be fully considered. Comprehensive management measures should be taken to achieve a win - win situation of increasing carbon sinks and protecting other ecosystem services, promoting the sustainable development of ecosystems and the improvement of human wellbeing.

According to the stochastic forest model, the net C O 2 emissions (supply) of the surplus provinces and (demand) of the deficit provinces in 2022 under the context of voluntary trading are −6.78 × 10^11 kgCO₂ and 6.71 × 10^11 kgCO_2, respectively. The net carbon emissions of the surplus and deficit provinces in 2022 are −6.26 × 10^11 kgCO₂ and 741 × 10^11 kgCO₂, respectively (Figure 11). The net carbon emissions in the carbon surplus provinces increased by 8.31 % . The net carbon emissions of the carbon deficit provinces decreased by 9.45 % . The effectiveness of the carbon emission rights resource trading model in realizing the horizontal carbon ecological compensation mechanism in the Yellow River Basin was verified. This result is consistent with those of previous studies. Wang noted that reasonable planning of the carbon emission trading market can effectively reduce carbon emissions (Wang R. et al., 2022). However, this conclusion contrasts with Lin’s conclusion that the effectiveness of carbon emission trading in limiting emissions in China is not through a market mechanism but rather through government intervention, which leads to significant carbon emission reduction (Lin and Huang, 2022). We believe that this discrepancy may stem from market participants’ initial lack of experience and understanding of the carbon trading market, which may affect their participation and trading behaviour. However, over time, as the market matures, the carbon emission rights resource trading market mechanism is expected to show greater effectiveness.

First, the practicality of the evolutionary game model constructed in this study could be affected by the interaction of different variables. The analysis conducted here examines the influence of individual variables such as the carbon ecological environmental governance costs, governance benefits, central government compensation and penalties, and oversight costs in the carbon deficit provinces. It does not account for potential cross-effects among these variables. Future research could build a more complex model to analyse the different scenarios comprehensively.

Additionally, this study used a random forest model to forecast the decrease in CO₂ emissions in each YRB province once the carbon ecological compensation mechanism was implemented through a voluntary trading system without a control group. This demonstrates how well the YRB’s horizontal carbon ecological compensation system works. In order to increase prediction accuracy and model resilience, future studies should look at ensemble approaches by combining machine learning techniques like random forests, support vector machines, and neural networks

In summary, this study establishes a solid foundation for future research endeavours. Future studies could develop more intricate models, encompass a broader array of variables, and establish a stronger bridge between theoretical constructs and practical applications.

This study used a machine learning model for predictive analysis to assess the effectiveness of the horizontal ecological compensation mechanism in the YRB. The horizontal CO₂ ecological compensation mechanism in the YRB seems to affect CO₂ deficit provinces more than carbon surplus provinces, when both absolute and relative values are taken into account. This observation suggests that the mechanism has a stronger promoting effect on reducing CO₂ emissions in deficit provinces. The enhanced promotion effect in carbon deficit provinces can be attributed to several factors. First, these provinces face greater economic pressure, as they need to pay more compensation to balance their CO₂ emissions and sinks. This economic burden motivates them to adopt more aggressive measures to reduce CO₂ emissions, such as investing in renewable energy technology, improving energy efficiency, and adopting CO₂ capture and storage technology. Second, to reduce CO₂ deficits effectively, CO₂ deficit provinces may implement stricter environmental protection policies. These policies strive for long-term economic and social change toward green and low-carbon development in addition to short-term objectives. Additionally, carbon deficit provinces often rely more on fossil fuels, indicating greater potential and demand for adjusting their energy structure and developing clean energy. The endogenous motivation stimulated by the compensation mechanism may accelerate the transition from traditional to clean energy. On the other hand, although carbon surplus provinces perform relatively well in terms of CO₂ emissions, the difference between the predicted and actual net CO₂ emissions was small, with a limited increase in the actual and predicted values. These provinces have been effective in maintaining their current CO₂ sink levels but still need to increase their emission reduction potential. While helping carbon deficit provinces reduce their CO₂ emissions, the YRB’s horizontal carbon ecological compensation mechanism encourages carbon surplus provinces to increase their efforts to reduce CO₂ emissions. This approach enhances environmental quality, encourages the development of clean technologies, and helps reduce regional CO₂ emissions

Guarantee measures for the horizontal carbon ecological compensation mechanism in the YRB should be further explored to strengthen the implementation effect of the mechanism and ensure its long-term sustainability, robustness, and adaptability.

(1) Under the guidance of higher-level regulations such as the Yellow River Protection Law of the People’s Republic of China and the Regulations Governing Ecological Protection Compensation, legislation should be enacted for the horizontal carbon ecological compensation mechanism in the YRB. This legislation should include the establishment of trading rules for the voluntary CO₂ emission trading mechanism, as well as the delineation of the rights and obligations of the participants within this mechanism. To reach the objective of carbon neutrality, institutional assurances and legal support can be given by creating a trading system that promotes the preservation of the natural environment and the reduction of CO₂ emissions. This institutional framework encourages the reduction of CO₂ emissions and the restoration of carbon ecosystems by allowing all parties to actively participate in CO₂ emission trading in accordance with the rules. This strategy promotes the socioeconomic and ecological environments’ sustainable growth.