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This study presents a comprehensive quantification of carbon sequestration as well as CO2/CH4/N2O emissions reductions from terrestrial ecosystems based on multiple sources of data from literature, inventories, public databases and documents. The pathways considered ecosystem restoration and protection from being converted into cropland or built-up areas, reforestation, management with improved nitrogen use in cropland, restricted deforestation, grassland recovery, reducing risk from forest wildfire and others. Here we describe the cross-cutting methods that apply across all 16 NCS pathways. The definitions, detailed methods and data sources for evaluating individual pathways can be found in the Supplementary Information.Cross-cutting methodsBaseline settingWe set 2000 as the base year because the large-scale national ecological projects, such as the Grain for Green Project, were started since then. We first evaluate the historical mitigation capacity during 2000–2020, which is the first 20 years of implementing the projects. From this procedure we can determine how much mitigation capacity has been realized through the previous projects in the past two decades and to what extent additional actions can be made after 2020. Relative to the baseline 2000–2020, we then evaluate the maximum potentials of the NCS mitigation in the future 10 (2020–2030) and 40 (2020–2060) years, corresponding to the timetable of China’s NDCs: carbon peak before 2030 and carbon neutrality by 2060.The settings of baseline in this study are different from the existing assessments (2000s–2010s as a baseline and 2010–2025/2030/2050 as scenarios)1,22,23,27,28. Baseline sets the temporal and spatial reference for NCS pathway scenarios, which may have a great impact on the NCS estimates. Notably, NCS actions during 2000–2020 will have a great impact in the future periods, which we refer to as the ‘legacy effect’. The legacy effect itself, mainly reforestation, is independent of being assessed, but it is conceptually attributed to natural flux and excluded from future NCS potential estimates.Maximum potentialThe MAMP refers to the additional CO2 sequestration or avoided GHG emissions measured in CO2 equivalents (CO2e) at given flux rates in a period on the maximum extent to which the stewardship options are applied (numbers are expressed as TgCO2e yr−1 for individual pathways and PgCO2e yr−1 for national total) (Extended Data Fig. 1 and Supplementary Table 2). ‘Additional’ means mitigation outcomes due to human actions taken beyond business-as-usual land-use activities (since 2020) and excluding existing land fluxes not attributed to direct human activities1. The MAMP of CH4 and N2O are accounted by three cropland and wetland pathways (cropland nutrient management, improved rice cultivation and peatland restoration). We adopt 100 yr global warming potential to calculate the warming equivalent for CH4 (25) and N2O (298), respectively38,39 because these values are used in national GHG inventories, although some researchers have argued that using the fixed 100 yr global warming potential to calculate the warming equivalents may be problematic because they cannot differentiate the contrasting impacts of the long- and short-lived climate pollutants39. Because the flux rate of the GHG by ecosystems may vary with the time of recovery or growth, the MAMP may also change for different periods even given the same extent.The ‘maximum’ is constrained by varied factors across the NCS pathways. We constrain forest and grassland restoration by the rate of implementation, farmland red line and tree surviving rate (Extended Data Fig. 2). Surviving rate here is the ratio of the area with increased vegetation cover due to reforestation to the total reforestation area. The farmland red line refers to ‘the minimum area of cultivated land’ given by the Ministry of Land and Resources of China. It defines the lowest limit, and the current red line is ~120 Mha. It is a rigid constraint below which the total amount of cultivated land cannot be reduced. From this total amount, there is provincial farmland red line. This red line sets a constraint on the implementation of the NCS pathways associated with land-use change. We set the future scenario of farmland area that can be used for grassland or forest restoration on the basis of the provincial farmland red line. Basic farmland is closely related to national food security. By 2050, China’s population is predicted to decrease slightly, but with economic development, the per capita demand for food may increase40. We assume that the food production in the future can meet the food demand via increasing agricultural investment and technological advancement. The N fertilizer reduction scenario is set to be below the level 60%, under which crop yield is not significantly affected19, because N fertilizer is surplus in many Chinese croplands. For timber production, we assume that the demand for timber can be met if the production level is maintained at the level of 2010–2020 (83.31 million m3 yr−1). As deforestation of natural forests is 100% forbidden since 2020, the future timber will come mainly from tree plantations. For grazing optimization, we assume that livestock production is not affected by grassland fencing due to refined livestock management such as improving feed nutrient and fine-seed breeding41.The areas of historical NCS implementation during 2000–2020 were estimated using statistical data, published literature and public documents, with a supplement from remote-sensing data. The flux rates were obtained either by directly using the values from multiple literature sources or from estimates using the empirical formulae. For the estimates of future NCS potential, the flux rate and extent of the pathway were determined on the basis of the baseline (2000–2020). The extent is assumed to be achieved by using the same rate but limited by the multiple constraints stated in the preceding unless the implementation scopes have been reported in national planning documents. We estimate the legacy effect by multiplying the implementation area in the past by the flux rates in the future two periods.SaturationThe future mitigation potential that we estimate for 2030 and 2060 will not persist indefinitely because the finite potential for natural ecosystems to store additional carbon will saturate. For each NCS pathway, we estimate the expected duration of the potential for sequestration at the maximum rate (Supplementary Table 3). Forests can continue to sequester carbon for 70–100 years or more. Restored grasslands and fenced grasslands can continue to sequester carbon for >50 years. Forest-fire management and cover crops can continue to sequester carbon for 40–50 years or more. Sea grasses and peatlands can continue to sequester carbon for millennia. Avoided pathways do not saturate as long as the business-as-usual cases indicate that there are potential areas for avoided losses of ecosystems. In this case, sea grass and salt marsh would disappear entirely after 64 years, but it would be 100–300 years or more for forest, grassland and peatland.Estimation of uncertaintiesThe extent (area or biomass amount) and flux (sequestration or reduced emission per area or biomass amount in unit time) are considered to estimate uncertainty of the historical mitigation capacity or future potential for each NCS pathway. We use the IPCC approaches to combine uncertainty42. Where mean and standard deviation can be estimated from collected literature, 95% CIs are presented on the basis of multiple published estimates. Where a sample of estimates is not available but only a range of a factor, we report uncertainty as a range and use Monte Carlo simulations (with normal distribution and 100,000 iterations) to combine the uncertainties of extent and flux (IPCC Approach 2). The overall uncertainties of the 16 NCS pathways were combined using IPCC Approach 142. If the extent estimate is based on a policy determination, rather than an empirical estimate of biophysical potential, we do not consider it a source of uncertainty.MACsThe economic/cost constraints refer to the amount of NCS that can be achieved at a given social cost. The MAC curve is fitted according to the total publicly funded investment and total mitigation capacity or potential during a period. The MAC curves are drawn to estimate the historical mitigation or MAMP at the cost thresholds of US$10, US$50 and US$100 (MgCO2e)−1, respectively. The trading price in China’s current carbon market is ~US$10 USD (as the minimum cost43), and the cost-effective price point44,45 to achieve the Paris Agreement goal of limiting global warming to below 2 °C above pre-industrial levels is US$100 (as the maximum cost). A carbon price of US$50 is regarded as a medium value1,46. For the pathways of reforestation, avoided grassland conversion, grazing optimization and grassland restoration, we collected the statistical data of investments in China from 2000 to 2020 and estimated the affordable MAMP below the three mitigation costs. Due to data limitations, the points used for fitting the MAC curve are values for cost (invested funds) and benefit (mitigation capacity) in each of the provinces. We rank the ratio of benefit to cost in a descending order to obtain the maximum marginal benefit for MAC by assuming that NCS measures are first implemented in the region with the highest cost/benefit rate. We refer to the investment standard before 2020 as the benchmark and estimate the cost of each pathway for the future periods with discount rates of 3% and 5%, respectively. The social discount rate 4–6% is usually used as a benchmark discount value in carbon price studies in China compared with lower scenarios (for example, 3.6%)46,47. In a global study for estimating country-level social cost of carbon, 3% and 5% are used for scenario analysis48. Note that the mean value from the two discount rates was used in presenting the results. For the other pathways where investment data cannot be obtained, we refer to relevant references to estimate MAC. All the cost estimates are expressed in 2015 dollars, transformed on the basis of the Renminbi and US dollar exchange rate of the same year. The year 2015 represents a relatively stable condition of economic increase over the past decade (2011–2020) in China (the increase rate of gross domestic product (GDP) in 2015 is similar to the 10 yr mean). In the cases when the MAC curves exceed the estimated maximum potentials in the period, we identify the historical capacity or the MAMP as limited by the biophysical estimates.Additional mitigation required to meet Paris Agreement NDCsOn 28 October 2021, China officially submitted ‘China’s Achievements, New Goals and New Measures for Nationally Determined Contributions’ (‘New Measures 2021’ hereafter) and ‘China’s Mid-Century Long-Term Low Greenhouse Gas Emission Development Strategy’ to the Secretariat of the United Nations Framework Convention on Climate Change as an enhanced strategy to China’s updated NDCs (first submission in 2015). The goal of China’s updated NDCs is to strive to peak CO2 emissions before 2030 and achieve carbon neutralization by 2060. It specified the goals to include the following: before 2030, China’s carbon dioxide emissions per unit of GDP are expected be more than 65% lower than that in 2005, and the forest stock volume is expected to be increased by around 6.0 (previously 4.5) billion m3 over the 2005 level. In the ‘New Measures 2021’9 and ‘Master Plan of Major Projects of National Important Ecosystem Protection and Restoration (2021–2035)’5, many NCS-related opportunities are proposed to consolidate the carbon sequestration of ecosystems and increase the future NCS potential, including protecting the existing ecosystems, implementing engineering to precisely improve forest quality, continuously increasing forest area and stock volume, strengthening grassland protection and recovery and wetland protection and improving the quality of cultivated land and the agricultural carbon sinks.Industrial CO2 emissionsThe historical CO2 emissions data from 2000 to 201749,50 are used as the benchmark of industrial CO2 emissions during 2000–2020. For future projections, we use the peak value of the A1B2C2 scenario (in the range of 10,000 to 12,000 Mt) in 2030 from ref. 11. We assume that CO2 emission increases linearly from 2017 to 2030.Characterizing co-benefitsNCS activities proposed in the future measures or plans may enhance co-benefits. Four generalized types of ecosystem services are identified: improving biodiversity, water-related, soil-related and air-related ecosystem services (Fig. 1). Biodiversity benefits refer to the increase in different levels of diversity (alpha, beta and/or gamma diversity)51. Water, soil and air benefits refer to flood regulation and water purification, improved fertility and erosion prevention, and improvements in air quality, respectively, as defined in the Millennium Ecosystem Assessment52. The evidence that each pathway produces co-benefits from one or more peer-reviewed publications was collected through reviewing the literature (see the details for co-benefits of each pathway in Supplementary Information).Mapping province-level mitigationThe data for extent of implementing forest pathways are obtained from the statistical yearbook and reported at the province level. To be consistent with the forest pathways, the other pathways were also aggregated to the provincial-level estimate from the spatial data. If the flux data were available in different climate regions, the provinces are first assigned to climate regions. When a province spans multiple climate zones, the weight value is set according to the proportion of area, and finally an estimated value of rate was calculated (for fire management, some grassland and wetland pathways). For the forest pathways, we first collected the flux-rate data from reviewing literature and then averaged these flux rates to region/province. The flux rates for reforestation and natural forest management were calculated separately by province and age group. Similarly, specified flux rates are applied for different times after ecosystem restoration or conversion for other pathways.Classification of NCS typesThree types of NCS pathways were classified: protection (of intact natural ecosystems), improved management (on managed lands) and restoration (of native cover)35. In our study, four (AVFC, AVGC, AVCI, AVPI), eight (IMP, NFM, FM, BIOC, CVCR, CRNM, IMRC, GROP) and four (RF, GRR, CWR, PTR) NCS pathways were identified as protection, management and restoration types, respectively (Supplementary Table 1). These pathways can be further divided into groups of ‘single’ type or ‘mixed’ type according to their contribution to individual pathways. Specifically, in a certain area, when the mitigation capacity of a certain pathway accounts for more than 50% of the total, it is regarded as a single or dominant NCS type; if no single pathway accounts for more than 50%, it is a mixed type, named by the top pathways whose NCS sum exceeds 50% of the total mitigation capacity. More

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Statistical characteristics of rill cross-sectional asymmetry (RCA)The rill cross-sectional asymmetry (RCA) is a key parameter in describing rill morphology and includes the asymmetry ratio of the width (Aw) and the asymmetry ratio of the area (Aa). It reflects the differences in certain aspects of natural conditions resulting in inconsistent development speeds on both sides of a rill cross-section. The cross-section was classified as left-biased if Aw, Aa < 0, quasi-symmetrical if Aw, Aa = 0, and right skewed if Aw, Aa > 0. The left/right deflection reflects that erosion on the right happened faster than on the left, so the slope on the left is not as steep as on the right. The results of this study show that asymmetry is a common phenomenon in the cross-section of a rill. The Aw ranged from − 1.77 to 1.97, with an average value of − 0.034. There were 374 cross-sections whose RCA was less than or equal to 0, meaning that 53% of the cross-sections were right-biased. The Aa ranged from − 1.81 to 1.71, with an average of − 0.046. There were 374 cross-sections with an RCA of less than or equal to 0, meaning that 53% of the cross-sections were right-biased (Fig. 1).Figure 1Statistical characteristics of the rill cross-sectional asymmetry (RCA).Full size imageFigure 2 shows that there are four Aw groups in the interval (− 1.7, − 1.5), 53 groups in the interval (− 1.5, − 1.0), 144 groups in the interval (− 1.0, − 0.5), 173 groups in the interval (− 0.5, 0), 174 groups in the interval (0, 0.5), 120 groups in the interval (0.5, 1.0), 39 groups in the interval (1.0, 1.5), and five groups in the interval (1.5, 2). The Aa has 15 groups in the interval (− 1.8, − 1.5), 63 groups in the interval (− 1.5, − 1.0), 130 groups in the interval (− 1.0, − 0.5), 166 groups in the interval (− 0.5, 0), 161 groups in the interval (0, 0.5), 110 groups in the interval (0.5, 1.0), 53 groups in the interval (1.0, 1.5), and 14 groups in the interval (1.5, 2). The RCA of most cross-sections is concentrated in the interval (− 0.5, 0.5). This interval of Aw contains 491 cross-sections, accounting for 68.96% of the total. There are 470 cross-sections in this interval of Aa, accounting for 66.01% of the total. This indicates that, although the rill cross-section exhibits some asymmetry, the difference between both sides of the section is small (Fig. 2).Figure 2Distribution characteristics of the RCA.Full size imageThe influence of a single topographic factor on the RCACorrelation analyses of the Aw, Aa, and the slope difference on both sides (B), rill length (L), rill slope length (I), rill head catchment area (A), difference between the catchment areas of both sides (R), rill bending coefficient (K), and location of the section angle of turning of the rill (J) were carried out. The results show that the main factors that have a significant linear correlation with the Aw and the Aa are B (p < 0.01), with correlation coefficients of 0.32 and 0.22, respectively (Fig. 3). That is, the greater the difference in slope between the two sides, the more asymmetric the rill cross-section. R also has a significant linear correlation with the Aw (p < 0.05), with a correlation coefficient of 0.07. This means that the greater the difference in the catchments between the left and right sides of the rill, the greater the asymmetry of the rill cross-section. However, other topographic factors have no significant correlation with the RCA.Figure 3Correlation between rill cross-sectional asymmetry (RCA) and topographic factors.Full size imageB is the difference in slope between the left and right sides of the rill cross-section catchment area. The closer B gets to 0, the smaller the difference in slope between the left and right sides of the rill cross-section catchment area. When the catchment area slope on the right side of the cross-section is greater than that on the left side, B < 0; and when the catchment area slope on the left side of the cross-section is greater than that on the right side, B > 0. Grouping B reveals that the average RCA increases as B increases (Fig. 4). When B is (− 30, − 20), Aw is − 0.48 and Aa is − 0.38; when B is (− 20, − 10), Aw is − 0.36 and Aa is − 0.31; when B is (− 10, 0), Aw is − 0.23 and Aa is − 0.22; when B is (0, 10), Aw is 0.21 and Aa is 0.16; when B is (10, 20), Aw is 0.47 and Aa is 0.40; and when B is (20, 40), Aw is 0.31 and Aa is 0.13. These are relatively low values because this group only has two sets of cross-sections which cannot represent the characteristics of interval B. The sign of the RCA is the same as the sign of B. The directionality of the RCA is significantly affected by B. When the slope of the left catchment area is large, RCA > 0, and the rill cross-section appears to be left-biased; when the slope of the right catchment area is large, RCA < 0, and the cross-section appears to the righ-biased.Figure 4The asymmetry of different B values.Full size imageThe influence of multiple topographic factors on the RCAIn order to explore the influence of multiple topographic factors on the RCA, principal component analysis (PCA) was used to extract the main feature components of the topographic data. The PCA results show that the nine topographic factors can be reflected by two principal components at 61.84% (characteristic value: 3.117+1.211=4.328 variables) (Table 1). Therefore, the analysis of the first two principal components could reflect most of the information from all the data.Table 1 Calculation results of topographic factor principal component analysis (PCA).Full size tableThe contribution rate of the first principal component is 44.534%. The characteristic is that the factor variables have high positive loads for the four factors L, I, A, and K. L has the largest contribution rate at 88.5%, followed by A, I, and K, at 87.5%, 81.1%, and 60.2%, respectively. Therefore, the first component represents the rill slope and rill shape.The contribution rate of the second principal component is 17.303%. The characteristic is that the factor variables have high positive loads for the three factors B, J, and R. B has the largest contribution rate at 83.5%, followed by J and R, at 57.4% and 55.7%, respectively. Therefore, the second component represents the effect of the difference between the two sides of the rill.Based on the correlation between the topographic factors and the RCA of a rill cross-section in the Yuanmou dry-hot valley area, the following was observed: asymmetry in rill cross-sections is ubiquitous. The distribution range of Aw is − 1.77 to 1.97, the average value is − 0.034, and the cross-section that is right-biased accounts for 53%. A correlation analysis of the RCA and seven topographic factors shows that B has a significant positive correlation with the Aw and Aa (p < 0.01), the average RCA increases as B increases, and the directionality of the RCA is affected by B. When B > 0, RCA > 0, and the rill cross-section appears to the left; when B < 0, RCA < 0, and the cross-section appears to the right. The difference in catchment area between the sides has a significant linear correlation with the Aw (p < 0.05). Other single topographic factors have no significant correlation with the RCA. Principal component analysis and calculations show that the first principal component represents the influence of the rill slope surface and rill shape on the rill cross-sectional asymmetry. The contribution rate is 44.534%, which is characterized by a high positive load on the L, I, A, and K factors. The second principal component represents the effect of the difference between the two sides of the rill. The contribution rate is 44.534%, which is characterized by a high positive load on the B, J, and R factors. More

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