## Introduction

Keeping the global temperature increase below 1.5 °C in accord with the Paris Agreement would require prompt and substantial reductions in greenhouse gases (GHGs) emissions on the global scale1. Despite considerable effort internationally, many countries are likely to miss the emission control targets proposed in the Paris Agreement. The world is on track for more than 3 °C of warming by the end of the century2,3. Numerous policies have long been proposed to cut down GHGs emissions, including resorting to renewable energy, popularizing electric vehicles, optimizing land-use policies, as well as other GHGs cutting policies or programs1,4. Unfortunately, those policy options seem not being effectively deployed, given the continuous increase of the emissions of GHGs5,6. The atmospheric CO2 has risen beyond 400 ppm in recent years, which is attributed to carbon emissions from fossil fuel combustion and explains the 1.5 °C increase in air temperature since the 1880s7,8.

Though cutting fossil fuel consumption provides a direct option to reduce carbon emissions, it shows limited effect in mitigating atmospheric CO2 because fossil energy still powers the economy in many countries4,9. Vegetation dominates most terrestrial ecosystems (e.g., forests, grasslands, croplands, shrublands, and savannas) and absorbs 112–169 PgC each year from the atmosphere through a biochemical process called photosynthesis8,9. Improving vegetation carbon sequestration provides an alternative measure to counteract the excessive carbon emissions9,10. The net amount of carbon captured by plants through photosynthesis over a given period is called net primary production (NPP)11,12. NPP is closely related to a carbon sink, which is equivalent to NPP minus the component of soil heterotrophic respiration13; thus, NPP serves as a good proxy for evaluating carbon sink. As a key component of energy and mass transformation in terrestrial ecosystems, NPP depends on various factors, such as the supply of nutrients, water availability, soil profile characteristics, and landscape attributes (e.g., terrain and drainage)14,15. Those factors can be broadly categorized as the following three groups16: (1) climate impact (e.g., precipitation and temperature); (2) nonclimatic natural factors such as soil property, landforms, and biomes; and (3) human-related (HUMAN) land-management practices.

First, vegetation will not attain the saturation of carbon sequestration capacity without appropriate climatic conditions10. Lack of rainfall causes physiological stress and limits vegetation photosynthesis in most arid regions14. The dependence of vegetation carbon sequestration on climatic factors is reflected by most NPP models11. For example, the climate-driven Miami model, which has been widely applied to map large-scale NPP10,17,18, highlights the climatic factors’ importance as vital drivers to carbon sequestration. Second, vegetation cannot maximize carbon sequestration without favorable natural conditions such as landforms15, soil properties19, and biome groups10. Lastly, carbon sequestration can be updated by land-management practices (LMPs)9, i.e., one LMP may result in higher or lower carbon sequestration than the other, under the same environmental contexts (the climatic and nonclimatic conditions).

Previous studies confirm that land use and management strategies have a massive effect on carbon sequestration from vegetation18,20,21. An optimal land-management practice (OLMP) refers to an LMP that helps sequester higher, if not the highest, potential carbon from the managed vegetation given the current climatic, nonclimatic, and HUMAN conditions. Once LMPs are replaced with OLMPs, the vegetation will sequester more carbon. It is valuable to model the difference in carbon sequestration between with and without OLMPs, called carbon gap hereafter, to make smart land-management policies and mitigate global climate changes. In a broad sense, OLMPs include removing negative human-related disturbances in naturally vegetated areas21, and applying human-intervened programs/practices that help improve vegetation productivity or restore previously degraded vegetation22,23. The United Nations Convention to Combat Desertification program introduces over 1000 sustainable land-management practices based on the type of activities targeting to promote agricultural production while simultaneously supporting the environmental functions24. OLMPs include but are not limited to sustainable land-management practices, considering that all existing LMPs could be potentially selected as OLMPs if they help enhance vegetation productivity. For example, appropriate tillage practices on cropland may increase agricultural production (which in most cases also improves NPP); similarly, protection measures for trees close to road networks are necessary to improve forestry NPP25. Some cases of OLMPs are illustrated in Supplementary Table 1. The impact of OLMPs on vegetation productivity pertains to local environmental and socio-economical contexts. The carbon gap of specific OLMPs can be evaluated by comparing NPP of field experiments with and without the OLMPs implemented. Because the global natural and socioeconomic contexts exhibit manifest spatial variations, there are no universally applicable OLMPs. There is also a need for mapping carbon gaps through a globally and locally consistent approach so that both global comparison and local policy enactment are supported26. This work addresses the following questions: how much more carbon (i.e., carbon gap) could be further sequestered from global terrestrial vegetation with OLMPs implemented? How can the location-dependent OLMPs be decided from the local contexts at each location? Where do the most sensitive areas showing carbon sequestration improvement locate?

## Results

### Global carbon gap modeling and mapping

The temporally averaged total carbon gap (during 2001–2018) for the vegetated land area is estimated to be 13.74 PgC yr−1, with a spatially averaged carbon gap flux density of 124.3 gC m−2 yr−1 (Supplementary Table 2). Considering that the terrestrial NPP totaled 67.90 PgC yr−1, ~1/5 more carbon can be added to the existing vegetation carbon sequestration if OLMPs are implemented. It was reported that the global fossil fuel emissions in 2019 were about 10.1 ± 0.6 PgC4. When the ratio of soil heterotrophic respiration (RH) to NPP is about 0.71~0.74 (see “Methods”), the total carbon gap of 13.74 PgC yr−1 means reducing an extra 3.5~4.0 PgC yr−1 from the atmosphere and compensating more than 1/3 of the global fossil fuel emissions. Fossil CO2 emissions in China, the United States of America (USA), and the European Union (EU28) contribute more than half of the global total, amounting to 2.75, 1,47, and 0.93 PgC in 2018, respectively4. Our analysis reveals that China, USA, and the EU28 could sequester an extra 0.29–0.32, 0.40–0.45, and 0.26–0.29 PgC in 2018 from the atmosphere by introducing OLMPs, accounting for 11–12%, 28–31%, and 27–31% of the fossil CO2 emissions, respectively.

The terrestrial carbon gap flux showed significant spatial variations (Fig. 1). Locations with higher carbon gap density indicate that their current LMPs are highly recommended to be replaced with the OLMPs identified from their neighborhoods, aiming to improve NPP and thus narrow down the carbon gap. OLMPs could take different forms depending on the local environmental and social conditions (with typical examples illustrated in Supplementary Table 1). The above-mentioned LMPs, if proved to be effective in improving vegetation productivity historically and thus called OLMPs, can promote vegetation carbon sequestration once transferred/copied to neighboring locations with identical local conditions and lower NPPCR, or the climate-rectified NPP (see “Methods”). Conversely, in grassland ecosystems where degraded vegetation showed decreased productivity due to overgrazing27, measurements such as destocking rate or rotational grazing in a neighborhood could increase vegetation productivity9,28; thus, the practices of destocking and rotational grazing can be taken as OLMPs.

### The carbon gap differs among continents and biomes

Considerable differences in the flux density of the carbon gap and NPP were observed among the 12 continents/regions (Fig. 2 vs. Supplementary Fig. 2). The total carbon gap and NPP of the continents/regions are summarized in Table 1. Central America and Southeast Asia present the highest carbon gap flux, reaching 348.3 and 260.7 gC m−2 yr−1, respectively; they can capture an extra portion of 0.17 and 1.11 PgC every year, respectively. Africa and North America have the largest vegetated area, and they can capture an extra 2.37 and 1.86 PgC yr−1, respectively. South America ranks the third-largest in the vegetated area (i.e., 16.58 million km2); because of its relatively high carbon gap flux which amounts to 167.6 gC m−2 yr−1, the carbon gap totals 2.78 PgC yr−1, leading all the continents/regions. The total carbon gap is strongly correlated to the total NPP at the continental/regional level (r = 0.98) (Table 1). However, the carbon gap flux (density) is inconsistent with the NPP density at the pixel scale and within each continent/region. At the pixel level, the carbon gap flux and NPP flux are compared by the ratio, i.e., the carbon gap flux divided by the NPP flux at pixel basis, which clearly shows the high spatial variations (Supplementary Fig. 3). Furthermore, within each continent/region, the carbon gap density (Fig. 1) and NPP density (Supplementary Fig. 2) do not correlate well. This finding is confirmed by the scatter plots between the carbon gap density vs. NPP density (Supplementary Fig. 4) and notably illustrated by two typical rainforests, i.e., the Amazon rainforest located within South America and the African rainforests (Supplementary Fig. 5). Both the rainforests show highly dense NPP fluxes (1273.3 and 1062.7 gC m−2 yr−1 for Amazon and African rainforests, respectively). These fluxes nearly double the globally averaged NPP flux (614.2 gC m−2 yr−1); however, their carbon gap flux averages 117.5 and 121.1 gC m−2 yr−1, respectively, at a comparable level to that of the continentally averaged level, i.e., 124.3 gC m−2 yr−1. The carbon gap varies among different biomes (see definition in Supplementary Table 3 and Supplementary Fig. 6). Grasslands and croplands disclose the maximum carbon gap density, reaching 138.3 and 137.2 gC m−2 yr−1, respectively (Fig. 3). Forests show somewhat limited potential in the carbon gap, only 107.99 gC m−2 yr−1 in the flux and 2.64 PgC yr−1 in the total, though the forests NPP flux almost doubles the global averaged (1106.2 gC m−2 yr−1 vs. 614.2 gC m−2 yr−1). The total NPP of forests is more than 1/3 of all other vegetation types together (i.e., 27.04 PgC yr−1 vs. 67.9 PgC yr−1) (Fig. 3 and Supplementary Fig. 7). The other woody vegetation (OWV), though presenting much lower NPP flux and total NPP, shows a carbon gap flux and total carbon gap comparable to those of forests, which are 107.4 gC m−2 yr−1 and 2.75 PgC yr−1, respectively. Because grasslands cover the largest area (46.97 million km2, Supplementary Table 4) and present the highest carbon gap flux, i.e., 138.3 gC m−2 yr−1, the total carbon gap accounts for nearly half of the all summed total, reaching 6.5 PgC yr−1. Croplands can sink atmospheric CO2 with the adoption of improved context-specific land management29. Croplands show relatively high carbon gap flux, 137.2 gC m−2 yr−1. However, croplands cover the least land area (13.52 million km2), making the total carbon gap the lowest, i.e., 1.86 PgC yr−1 only.

The carbon gap flux presents a strong clustering pattern, which is reflected by the comparison between the accumulative carbon gap and the accumulative sliced vegetated area using the carbon gap flux from low to high (Fig. 4 and Supplementary Fig. 8). On average, ~50% of the total carbon gap comes from only ~15% of the global vegetated area. In terms of OLMP implementation, the finding suggests that only a small part of the prioritized vegetated area, i.e., ~15% of total vegetated coverage, would add more 6.87 PgC yr−1 (i.e., 50% of the total carbon gap) in vegetation productivity.

### Human activities strongly affect the carbon gap

We examine the relationship between the carbon gap and the population, as human density is a good indicator of human activities30. The world population varies substantially over the space between continents/regions (Fig. 5 and Supplementary Table 5). South Asia, East Asia, and Southeast Asia present the most densified population, followed by moderately populated Southwest Asia, Europe, and Africa. At the global level, there exists no close link between the carbon gap flux and population density (Pearson’s correlation coefficient r = 0.27; see Supplementary Table 5). However, they demonstrate strong correlations at the continental/regional scale. The β coefficients of their regression lines are positive and statistically significant over all the continents (Table 2 and Supplementary Fig. 9). The goodness of fit of the regression models (R2) differs probably due to the varied spatial configuration in population distribution and biophysical environments reflected by LVS factors. The findings suggest that the areas with intensive human influences are more likely to note high carbon gap flux, primarily observed in densely populated areas (Figs. 1 and 5). At the same time, the impact on the carbon gap from human activities is not independent of the biomes distribution, which is noticeably observed in the plain region of Eastern China and some plain regions of India presenting the most densely populated but relatively lower carbon gap flux (Figs.  1 and 5). Those plain regions show relatively low NPP flux (Fig. 5 and Supplementary Fig. 2), and thus the carbon gap density will also be low (see “Methods”). One explanation is that these plain regions have long been cultivated. These regions’ crop production management practices are well optimized and fit their environments. In other words, these regions have realized OLMPs to some extent. Therefore, the NPP variability is very limited in these regions. As a case of human activities, updating LMPs can alter vegetation NPP in terrestrial ecosystems, either positively or negatively22,28. The study verifies that human activities have generally increased the carbon gap in the past two decades and thereby, policy interference should focus more on those highly populated areas.

## Discussion

The Paris Climate Agreement proposed national contributions to the goal of holding global warming to well below 2 °C3. Assessing the carbon gap, i.e., how much more carbon is to be sequestered through optimal land-management practices (OLMPs), is helpful to mitigate climate changes. This study combines time-series remote sensing datasets, partitioned landscape–vegetation–soil (LVS) zones, and distance-constrained zonal analysis to identify OLMPs and assess the carbon gap (see “Methods”). We estimate that ~1/5 more carbon, totaling 13.74 PgC yr−1, could be added to the current NPP from global terrestrial vegetation if the identified OLMPs get implemented, or a net effect of reducing 3.5–4.0 PgC yr−1 from the atmosphere. On average, the carbon gap flux is 124.3 gC m−2 yr−1, with large variations among the continents/regions and the vegetation biomes. Central America and Southeast Asia present the highest carbon gap flux, reaching 348.3 and 260.7 gC m−2 yr−1, respectively. Grasslands show the most potential in improving carbon sequestration, with a carbon gap flux of 138.3 gC m−2 yr−1 and a total carbon gap of 6.5 PgC yr−1. Half of the total carbon gap concentrates in ~15% of the vegetated area, where particular policy-making attention needs to focus. In other words, location-dependent OLMPs should be prioritized to fill the carbon gaps, particularly in the ~15% areas with the highest potential.

Improving land-management actions can add to nationally determined contributions (NDCs) to the Paris Agreement31,32. Previously, it was reported that land use, land-use change, and forest (LULUCF) sector could contribute to as much as 20% of the mitigation potential of NDC targets at the global level33. Our study suggests the contributions from LULUCF to NDC targets might be greatly underestimated, as applying OLMPs alone can reduce more than 1/3 of the current global fossil fuel emissions. The net atmospheric carbon reduction from OLMPs varies among countries/regions, including China, USA, the EU28, and India, which have the most fossil carbon emissions or/and the largest population (Supplementary Table 6)4. As the largest population in the world, China emits the most total greenhouse gases in recent years4. China has declared to realize the peaking of carbon emissions around 2030 in its NDC under the Paris Agreement. Successfully fulfilling the NDC targets depends on substantial efforts to fully implement all current policies and adopt more effective policies after 202034. Implementing OLMPs could account for 11–12% of its current carbon emissions, which can play an important role in achieving the NDC target of the country. USA is one of the most developed countries having the second-largest carbon emission and has promised to achieve 26–28% emission reductions below the 2005 level in 2025 in its first NDC and 50–52% reductions in 2030 in the second. Implementation of OLMPs in USA will contribute 27–31% carbon emission reduction. As the world’s biggest economy and the third biggest carbon emitter, the EU28 recently set its NDC target to a net decrease in emissions by 55% from the 1990 level by 203035. The carbon gap through implementing OLMPs could contribute 28–31% reduction of the EU28’s fossil carbon emissions, compensating more than half of its NDC target. India is the world’s second-largest populated country which emitted 0.74 PgC in 2018. The NDC target from India pledges 33–35% reduction in the emissions intensity of its GDP from the 2005 level by 203036. Implementation of OLMPs can help India neutralize 15–16% carbon emissions at the level of 2018.

The varied carbon gap among different biomes provides essential information for designing OLMP implementation strategy. The higher carbon gap fluxes in grasslands and croplands indicate that they have a quicker or more sensitive response to human activities (i.e., updated LMPs) than the forests and OWV. For grasslands and croplands, vegetation productivity improvement (or degradation) may take a shorter period to appear (e.g., within a calendar year) once LMPs are updated. Conversely, apart from abrupt intervention from human activities such as massive reforestation or deforestation9, forests and OWV vegetation may take a relatively longer time to show up the effect from updated LMPs. Thus, grasslands and croplands have the advantage of showing immediate benefit, i.e., increased carbon sequestration, from the implementation of OLMPs. On the other hand, it requires a long-term plan to improve carbon sequestration for forest and OWV ecosystems.

OLMPs correspond to one or a set of LMPs that have historically proved to be able to produce higher NPPCR (≥90th percentile of NPPCR) at locations within an environmentally (climatically and non-climatically) homogeneous neighborhood. In the farm-dominated regions, LMPs such as cropping rotation, farm irrigation, or compost amendments effectively improved agriculture productivity9. Multiple cropping, fertilizer application, and irrigation in China and India’s agricultural lands had contributed to the greening Earth as a result of an observed increase in green leaf area37. Cover crops are commonly included in strategies aimed at increasing agricultural production38. Planting cover crops play an important role in improving the productivity of subsequent crops39. Reforestation, or planting trees in areas that have been degraded or deforested, can promote restoration of forest structure and vegetation productivity by regrowing tree canopy and preserving biodiversity, thus improve carbon sequestration40. The previous study suggests that land-cover transformation from one type to another, e.g., afforestation from croplands, can sequester more carbon22. However, while afforestation has been suggested for degraded croplands22,23, concerns arise from decreased food supply due to a reduction in croplands resulting from afforestation. Hence, improving carbon sequestration through land conversions is not widely acceptable. Instead, it achieves more ecological and social benefits to obtain the carbon gap by tailoring land-management practices (i.e., by adopting OLMPs) without changing land use or land-cover types. Moreover, the referenced OLMPs are located within a neighborhood of ~20 km, which provides convenience for field verification and result evaluation in OLMPs implementation.

Nevertheless, there are a few concerns that may cause uncertainties, requiring further improvement and exploration. First, the referenced target NPP, i.e., NPPCR90th, could come from optimal LMPs that induce extra GHGs emissions, e.g., N2O (for instance, fertilizer application in croplands). As a result, the net effect of mitigating GHGs through OLMPs in some areas could be overestimated. Conversely, because the GHGs mitigation is estimated based on historical LMPs, it is unrealistic to identify OLMPs that are not historically present, meaning that the estimated carbon gap is likely to be underestimated due to the lack of referenceable OLMPs. Second, while land-management optimization can achieve higher NPP (and vegetation carbon sequestration), an implementation of OLMPs for ecological benefits (i.e., more NPP and carbon sequestration) may contradict other socioeconomic needs e.g., maximizing the production of grains or other edible produces. Furthermore, implementing OLMPs could involve extra input (e.g., labor or other resources), offsetting the willingness to implement the OLMPs widely. Under those cases, the land-management optimization could be adjusted to a lower target potential NPP, e.g., from the current 90th percentile (NPPCR90th) to the 80th percentile, which will allow more candidates of OLMPs for options. Third, the relative contribution (RC, see definition in Eq. (2)) on NPP due to the climate variations could be biased. The assumption that the contribution from HUMAN impact is reflected in the spatial variation of the climate-rectified NPP (NPPCR) by subtracting RC from NPP in LVS zones, as shown in Eq. (3), may not hold due to possible interaction effect between the climate and HUMAN impact. Furthermore, though the Miami model provided a good approximation of the global distribution of potential vegetation productivity41, it is empirically based, which could produce a biased estimate of RC of the climate variations by Eqs. (1) and  (2). Improved methods capable of modeling the relative contribution of climate variations in LVS zones are undoubtedly helpful for a more accurate estimate of the carbon gap. Lastly, while the landscape–vegetation–soil (LVS)-based segmentation is designed to create biophysically homogeneous zones as the most important biophysical units for assessing carbon gap, the LVS segmented zones may not be internally homogeneous due to possible noises in the landforms (L), vegetation (V) cover, and soil (S) datasets. Notably, in areas such as mountainous regions (e.g., Himalayas and Andes), which are characterized by complicated landscapes, the relatively coarse spatial scale (500 m) of the datasets adopted in this study may not be able to capture the biophysical heterogeneity within an LVS zone. Such heterogeneity not expected in an LVS zone due to the lack of high-quality datasets at a global scale means more diversity in environmental conditions, resulting in higher NPP variability and higher NPPCR variability in the LVS zone. Thus, compared to many plain regions across the global terrestrial ecosystems, areas with complicated landscapes are more likely to present an overestimated carbon gap. In addition, some other complex factors, such as seasonal hydrologic pulsing42 and nitrogen deposition43, may affect vegetation productivity but were not included in the current design. As a result, the spatial variability in the biophysical environments related to NPP might not have been fully addressed by the LVS segmentation. Furthermore, wetlands were excluded in the analysis in the carbon gap. Vegetation in wetland ecosystems is sensitive to water depth variations (particularly in complex terrains close to water bodies and lakes)44, hydrologic alterations42, sediment and turbidity45, and even transferred pollutant elements46. The impacts of these hydrological processes on NPP are challenging to model at a global scale. Considering that wetlands cover only about ~1% of the total land area (see Supplementary Table 3), excluding wetlands should only have a limited impact on the globally estimated carbon gap patterns. Because the detailed biophysical and socioeconomic datasets (including LMPs) are rarely available at a global scope, the uncertainties raised from the lack of high-quality datasets are challenging to address in this work. We suggest that refined assessment of enhancing vegetation productivity through OLMPs be conducted at a national scale with the support of detailed socioeconomic contextual datasets and biophysical datasets for different terrestrial ecosystems. Nevertheless, the potential of improving carbon sequestration through OLMPs is confirmed, though designing practicable schemas for OLMPs implementation requires multiple participations from both governments and private sectors to work together.

## Methods

We divide the factors affecting vegetation carbon sequestration into three categories16:

1. 1.

Climate impact (typically precipitation and temperature)

2. 2.

Other nonclimatic environmental/natural factors, including landforms (L), vegetation (V) types, and soil (S) property

3. 3.

Human-related land-management practices (HUMAN)

Once the differed impact on vegetation carbon sequestration from the climatic (1) and nonclimatic (2) is excluded, the difference in the carbon sequestration from vegetation over space will be solely attributed to site-specific HUMAN (3) impact. We apply net primary productivity (NPP) to indicate the capacity of vegetation carbon sequestration in terrestrial ecosystems. The method is developed based on the following assumptions:

• NPP is jointly affected by (1) climate impact, (2) LVS (landscape–vegetation–soil) environmental or biophysical factors, and (3) HUMAN activities (land-management practices, LMPs).

• Over a homogeneous LVS segmented zone, the climate factors and HUMAN factors are the most important ones explaining the NPP variation in an LVS zone. The climate’s potential impact on vegetation productivity in an LVS zone can be indicated by climate-driven NPP models such as Miami, called potential NPP (PNPP).

• The variation of NPP from the differed climate factors in an LVS zone can be measured by a statistic called Relative Contribution (RC) of the climate factors. RC is the difference between PNPP at a location in an LVS zone and the averaged PNPP of the whole zone.

• RC is designed to rectify the relative impact of the climate factors on NPP over an LVS zone to derive climate-rectified NPP, or termed as NPPCR. The variation of NPPCR over the LVS zone is then attributed to HUMAN influence.

Our main objective is to assess how much more carbon (termed as carbon gap) can be realistically achieved from global terrestrial vegetation by updating HUMAN only, without converting land use and land cover or vegetation biomes. We use publicly available time-series of datasets to analyze the carbon gap. Data sources come from Google Earth Engine (GEE). Data preprocessing and analysis are also performed on the GEE computing platform. There are four groups of data sources involved, namely climate-related variables, (non-climate) physical environmental variables, NPP, and world population. Those datasets, if not at the scale of 500 m, are uniformly be resampled to a resolution at 500 m. The following explains the steps of data processing and analysis methods.

### Region segmentation of homogeneous natural environments to detach non-climate impacts on NPP variation

Region segmentation is performed by overlaying the layers of landform (L), vegetation type (V), and soil type (S) to derive homogeneous zones, known as homogeneous LVS zones so that all locations (image pixels) in an LVS zone will have the same LVS# of landform, vegetation, and soil type. In other words, over the pixels within the same LVS zone, the impact from the non-climate environmental factors on the internal NPP variation is uniform. Thus, any NPP variation within an LVS zone is attributed to varied climatic and HUMAN impacts only.

The three environmental factors, namely landforms, biomes types, and soil profiles, are chosen for LVS segmentation because of the following considerations. First, landform properties are often used to represent the spatial variability of hydrological, geomorphologic, and biological processes47. Here, we use the classified landform cover from European Soil Data Centre (https://esdac.jrc.ec.europa.eu) to indicate landform variations. This landform cover includes 16 labels dynamically classified by an unsupervised nested-means algorithm based on three geometric criteria (slope, surface texture, and local convexity) from the Shuttle Radar Topography Mission 30 m (SRTM30) digital elevation data48. Second, the International Geosphere-Biosphere Programme (IGBP) land-cover classification schema of MODIS MOD12Q1 (asset ID=MODIS/006/MCD12Q1 in GEE) is taken to map vegetation (biome) distributions. According to the IGBP land-cover classification system, there are 17 labels, out of which 13 are closely related to vegetation cover types. Five of them (13# urban and built-up lands, 15# snow and ice, 16# barren, 17# water bodies, and 11# permanent wetlands) are excluded from further analysis (Supplementary Fig. 6 and Supplementary Table 3). Wetlands have been shown to play an important role in global carbon exchange49. However, our exploratory analysis reveals that spatial variation of NPP in wetlands in most areas is huge, which we believe could not be explained simply by the biophysical environment differences indicated by LVS factors. We attribute the large NPP variation in wetlands to other factors such as variations in water depth (in complex terrains close to water bodies and lakes)44, hydrologic alterations42, sediment, and turbidity45, and even variations in pollutant elements transferred through water movement46. Furthermore, the wetlands area covers only about ~1% of the total land area (see Supplementary Table 3). Excluding wetlands should have a limited impact on the globally estimated carbon gap. Thus, only 12 land-cover classes were analyzed for sinking CO2 from the atmosphere in this study. Lastly, Harmonized World Soil Database (HWSD, ver. 1.2 from Food and Agriculture Organization, http://www.fao.org/soils-portal) is the most up-to-date world soil map that incorporates a data table of 48,148 soil profile descriptions related to the various soils associated with each mapping unit, at a spatial resolution 1 km at the equator50. Thus, soil-type classes from FAO-90 code (SU_Code90), which includes 194 labels, are used for mapping soil-type cover.

### Rectifying the climatic impact on NPP

NPP dataset provides a direct indicator of carbon sequestration from vegetation. The MODIS MOD17A2H product (V6) is a cumulative 8-day composite at 500-m spatial resolution. MOD17A2H includes a layer of net photosynthesis, an indicator of NPP reflecting the spatiotemporal variations in vegetation carbon sequestration.

In terms of the climatic factors, precipitation and temperature are the most important elements because both of them were confirmed to alter NPP and thus carbon uptake from vegetation51. Theoretical NPP has been modeled purely from climatic conditions; the climate-driven empirical Miami model is considered the first to compute PNPP using monthly precipitation and temperature and is often used as a baseline for model comparison52. The modeled PNPP exhibits many spatial variations, reflecting spatial heterogeneity of the impact of the climatic factors.

We assume that the Miami model can be applied to measure the relative impact on NPP from climate variations in an LVS zone. The Miami model is used to assess the climate impact on PNPP, which takes the form51,

$${{{{{\rm{PNPP}}}}}}= {\lambda}\times \min \left\{\frac{3,000}{1+{e}^{1.315-0.119t}},\,3,000\times (1-{e}^{-0.000664p})\right\}$$
(1)

where t is the annual average temperature (°C), p is the annual precipitation (mm), and ƛ is a conversion coefficient (0.50 for woody ecosystems and 0.45 for herbaceous) that converts dry matter to carbon unit (gC m−2 yr−1). TerraClimate derived from climatically aided interpolation by combining WorldClim dataset and Climatic Research Unit Time-Series dataset has been widely applied for mapping regional and global ecological parameters53. It provides monthly precipitation and maximum/minimum temperature at the spatial resolution of 2.5 arc minutes. Equation (1) describes the relationship between PNPP and two climatic variables, p and t.

For discriminating the varied climate impact on NPP in an LVS zone, a location-dependent relative contribution (RC) of climate factor is defined as the difference between PNPP at location i in an LVS zone g and the averaged PNPP of the whole g, namely,

$${{{{{\rm{RC}}}}}}(i,g)={{{{{\rm{PNPP}}}}}}(i,g)-{{{{{{\rm{PNPP}}}}}}}_{{{{{{\rm{Mean}}}}}}}(g)$$
(2)

where PNPP(i,g) is PNPP at i in g, PNPPMean(g) is the mean PNPP of all the locations in g, namely $${{{{{{\rm{PNPP}}}}}}}_{{{{{{\rm{Mean}}}}}}}(g)={\sum }_{i=1}^{{n}_{g}}{{{{{\rm{PNPP}}}}}}\left(i,g\right)/{n}_{g}$$ and ng is the total number of locations (pixels) in g. RC(i, g) is the difference between PNPP at i and PNPPMean(g) due to within-group variation of the climate impact. Clearly, $${\sum }_{i=1}^{{n}_{g}}{{{{{\rm{RC}}}}}}\left(i,g\right)=0$$. The rationale is that more favorable climate conditions at a location i will result in a positive and higher RC(i,g) and vice versa.

The climatic and HUMAN impact determine the NPP variations across an LVS zone characterized by the identical landform, vegetation cover, and soil properties. The assumption is that the climatic impact on NPP variations can be estimated by RC on a location basis in an LVS zone. Climate-rectified NPP (NPPCR) at location i in g can be derived using the function,

$${{{{{{\rm{NPP}}}}}}}_{{{{{{\rm{CR}}}}}}}(i,g)={{{{{\rm{NPP}}}}}}(i,g)-{{{{{\rm{RC}}}}}}(i,g)$$
(3)

NPPCR(i,g) is the rectified NPP at location i in g after the climatic impact on NPP is removed by applying Eq. (3). Considering $${\sum }_{i=1}^{{n}_{g}}{{{{{\rm{RC}}}}}}\left(i,g\right)=0$$, it is clear that $${\sum }_{i=1}^{{n}_{g}}{{{{{{\rm{NPP}}}}}}}_{{{{{{\rm{CR}}}}}}}\left(i,g\right)={\sum }_{i=1}^{{n}_{g}}{{{{{\rm{NPP}}}}}}\left(i,g\right)$$. In other words, the NPP distributions over g are readjusted to NPPCR by taking the zonal climate variations into account through Eq. (3). The internal variation of the computed NPPCR across all the locations in the LVS zone g will then be attributed to HUMAN impact only. Thus, after the climate rectification, NPPCR should be free of variations of the effect of climate factors in each LVS zone. NPPCR would assume a constant value if there were no differed HUMAN impacts within an LVS zone. When spatial variations of NPPCR within an LVS zone are observed, it is attributed to HUMAN influence, i.e., the difference in land-management practices (LMPs). Those locations showing low NPPCR are not managed well from the perspective of their current carbon sequestration. Particularly, for locations with negative NPPCR (NPPCR < 0), the HUMAN impact on NPP is negative. Thus, carbon gaps over these locations are considerable. On the contrary, the locations (pixels) showing relatively very high NPPCR values can be regarded where good LMPs are practicing. These good LMPs can be deemed to be the optimal LMPs (OLMPs) under similar environmental conditions over this LVS zone. The varied NPPCR in an LVS zone suggests that introducing the LMPs in the current LVS zone can sequester more carbon. In other words, through human policy and management interventions, the LMPs at locations (pixels) with lower NPPCR in the LVS zone could be replaced by the OLMPs at places with higher NPPCR to increase carbon sequestration to a higher level.

### Computing carbon gap by distance-constrained (DC) zonal analysis

The OLMPs and carbon gaps are processed for each location. The carbon gap at a given location is computed as the gap from its current NPPCR to a target NPP level that is the most achievable high NPPCR at locations with identical or similar environmental contexts (i.e., in the same LVS zone). We develop a distance-constrained zonal analysis to evaluate the target NPP level. Zonal analysis computes a set of statistics (e.g., maximum, median, or minimum value) from the input values of NPPCR within a zone54. The maximum zonal NPPCR (NPPCRMax) is the highest NPPCR corresponding to the best land-management practice (BLMP) in the zone; if BLMP is adopted, it will present the highest carbon gap. However, a zonal statistic defined as the 90th percentile, or NPPCR90th, from the input vector of NPPCR is selected as the referenced target NPP level in this study. The selection of NPPCR90th instead of NPPCRMax in an LVS zone can exclude exceptionally high NPPCR values, which are likely outliers resulting from noisy data, or are hardly achievable by other locations even in the same LVS zone. Thus, the zonal statistic NPPCR90th provides a more robust reference as the target potential NPP level. The LMPs at locations showing NPPCR ≥ NPPCR90th will be referenced as the OLMPs for other locations in a similar environmental context.

The appraisal of the NPPCR90th at a location is conducted among locations labeled as the same LVS# within a local neighborhood. It is argued that the variations of NPPCR at locations within an LVS zone are attributed to the differences in HUMAN impacts (i.e., LMPs). It is also acknowledged that other omitted factors may impose an unneglectable impact on vegetation carbon sequestration, which could produce certain uncertainties in the isolation of HUMAN impact. Thus, the determination of OLMPs is preferably performed at local scope. In other words, LMPs at locations too far away from the currently examined location could be affected by too many heterogeneous economic, social, and political factors. Furthermore, locally referenced OLMPs are more practical for policy implementation and make it possible for on-site checkout.

A window size specifies a local neighborhood surrounding given location i, in which the NPPCR values at all the locations with the identical LVS# in this window are taken as input to compute the NPPCR90th. To decide the window size, a stratified random selection approach is taken to sample 5000 points in the vegetated land with the sample size weighted by the area of each of the biome types. The samples’ histogram shows peak NPPCR90th along with the distance, which presents a relatively stable stage when the distance is over 20 km from the piecewise linear function fitting (Supplementary Fig. 1). Hence, the carbon gap at location i is computed as the difference between the current NPPCR and the NPPCR90th within the 20 km window in the environmentally homogeneous zone (i.e., LVS zone).

$${{{{{{\rm{Carbon}}}}}}\,{{{{{\rm{gap}}}}}}}_{{{{{{\rm{i}}}}}}}\,=\,{{{{{\rm{max}}}}}}(0,{{{{{{{\rm{NPP}}}}}}}_{{{{{{\rm{CR}}}}}}}}^{90{{{{{\mathrm{th}}}}}}}{{-{{{{{\rm{NPP}}}}}}}_{{{{{{\rm{CR}}}}}}}}^{{i}})$$
(4)

where NPPCR90th corresponds to the statistic of the 90th percentile for NPPCR input at all locations labeled as the same LVS# in the distance-constrained neighborhood, NPPCRi is NPPCR for location i, and max is the function for getting the maximum value from the two input 0 and NPPCR90th–NPPCRi, meaning that if the NPPCR at the location i is less than the NPPCR90th, the carbon gap will be equivalent to NPPCR90th minus NPPCRi; otherwise, the land-management practice (LMP) at location i has already reached the level of carbon sequestration under OLMP and no extra space of carbon sequestration is available (i.e., carbon gapi = 0, if NPPCRi ≥ NPPCR90th). The carbon gap is not only dependent on the NPPCR variability but also constrained by the level of NPPCR. It is reasonable that areas with a low NPP (and accordingly NPPCR) density cannot be expected to have a higher carbon gap density. Note that low NPP values in non-vegetated areas (corresponding to the IGBP land-cover types labeled as 13# urban and built-up lands, 15# snow and ice, 16# barren, 17# water bodies) which have been previously excluded are not used in the NPPCR90th computation. Thus, the candidate of OLMPs for a location is decided by referring to the LMPs within the distance-constrained local window that boast identical environmental contexts but exhibit a higher level of carbon sequestration (i.e., where NPPCR ≥ NPPCR90th).

The carbon gap flux and NPP flux are shown in Fig. 1 and Supplementary Fig. 2. The annual changes in the carbon gap and NPP are summarized in Supplementary Table 4. The ratio map of carbon gap density to NPP density is shown in Supplementary Fig. 3. The carbon gap and NPP (total and flux density, respectively) among the biomes and continents/regions are compared in Supplementary Fig. 7.

### Effect of reducing atmospheric CO2 from the carbon gap

The resultant carbon gap suggests an increase of NPP 13.74 PgC yr−1 with OLMPs implemented (Supplementary Table 2). When considering the possible increase in soil heterotrophic respiration (RH), the improved NPP’s net effect (i.e., the carbon gap) on reducing atmospheric CO2 is less than this total NPP. Previous studies show that the total amount of RH is mainly proportional to NPP; for example, the previous study showed that the ratio of RH to NPP was 0.7113. A meta-analysis on RH from the available dataset estimated that the global weighted mean RH was 457 ± 139 gC m−2 yr−1 55. Our study indicates that the average NPP over the study years is 614 ± 35 gC m−2 yr−1 (Supplementary Table 2), suggesting that the ratio of RH to NPP is 0.74 (=457/614), which is reasonably close to the previous study13. Taking the ratio of RH to NPP between 0.71 and 0.74 (though the ratio is subject to vary on a broader scope under climate changes), an increase of NPP (the total carbon gap) 13.74 PgC yr−1 is estimated to reduce 3.5–4.0 PgC yr−1 from the atmosphere.

### Correlation analysis between total carbon gap and total NPP

The relationship between the total carbon gap and total NPP at the global scale is revealed by Pearson’s correlation analysis on the two variables, i.e., total carbon gap and total NPP for each continent/region, resulting in Pearson correlation coefficient r = 0.98 (Fig. 2). The relationship between the carbon gap flux and NPP flux at the sub-continental/regional level is performed by slicing the carbon gap density into partitions based on the ordered percentiles of the carbon gap flux (from low to high) at an interval of 5%, i.e., 0–5%, 5–10%, …, and 95–100% for each continent/region (Supplementary Fig. 4). Comparison between the total carbon gap and total NPP for two typical regions, i.e., amazon rainforests and the rainforests of Africa, is further illustrated in Supplementary Fig. 5.

### Analyzing the distribution pattern of the carbon gap

For each of the 12 continents/regions, the carbon gap flux is grouped based on the sliced percentiles (from low to high) at an interval step of 5%, i.e., 0–5%, 5–10%, …, and 95–100%. The vegetated area and total carbon gap within each percentile are then computed. The points denoted by the accumulative vegetated area and the accumulative total carbon gap in each percentile are used to reveal the carbon gap’s clustering pattern (Supplementary Fig. 8). The maximum accumulative total carbon gap is divided into two half-half sections by a horizontal line, i.e., low flux density and high flux density. The global clustering pattern in the carbon gap distribution is similarly derived (Fig. 4).

### Regression analysis between carbon gap and population density

For each of the 12 continents/regions, the carbon gap density is grouped based on the sliced percentiles (from low to high) at an interval step of 5%, i.e., 0–5%, 5–10%, …, and 95–100%. We then compute the accumulative total carbon gap and accumulative total population. The relationships between the accumulative total population and the accumulative total carbon gap are graphed by the sliced percentiles. Linear regressions are fit for the partitions with the accumulative total carbon gap set as the dependent variable and the accumulative total population for each percentile as the independent variable (Table 2 and Supplementary Fig. 9).

The world population data comes from the Gridded Population of World (Ver. 4, from NASA Socioeconomic Data and Applications Center)56, which models the distribution of the global human population for the years 2000, 2005, 2010, 2015, and 2020 on 30 arc-second grid cells. A proportional allocation gridding algorithm, utilizing millions of national and sub-national administrative units, is used to assign population counts to 30 arc-second grid cells. The averaged population density and carbon gap flux within each continent/regions is summarized in Supplementary Table 5.

### Validation of the estimated carbon gap

Systematic validation of the estimated carbon gap is challenging because it requires long-term field experiments for different ecosystems and biomes across the globe. We test the result of the carbon gap on the typical grassland in the Inner Mongolia Autonomous Region (IMAR) in China based on long-term field monitoring of vegetation productivity under varied LMPs. As vegetation in IMAR has been reported to be degraded due to human activities, particularly overgrazing, many vegetation protection measures have been introduced57. For example, exclosure grazing excludes grazing from a protected area. Rotational grazing feeds animals in different fields in rotation depending on the forage condition. Both exclosure and rotational grazing are believed to be good strategies that have proved effective in protecting vegetation58. In addition, rest-grazing allows grazing fields to be rested and grazed on a rotational base. Reseeding is a measure to supplement grass seeds to improve vegetation density. These measures have also been proved to be OLMPs in the grassland. Those vegetation restoration measures have been implemented over the last two decades or so across the IMAR grasslands.

Grassland vegetation NPP can be quantified by the method using maximum peak live biomass59. A set of sites under the above-mentioned OLMPs, including exclosure grazing, rotational grazing, rest-grazing, and reseeding, have been selected across the pastoral counties in IMAR characterized by livestock grazing (Supplementary Fig. 10). Those sites under OLMPs are small fenced or protected areal patches. Vegetation productivities within and outside each site are compared to estimate the effectiveness of vegetation protection from the OLMPs. Within and outside each site stand for with and without implementation of the OLMPs, respectively. Aboveground biomass was collected in pairs, namely in and outside each protected area, at the time of peak vegetation growth in late August each year during 2009–2015, led by the Inner Mongolia Grassland Survey Institute. Estimating NPP from the maximum peak live biomass requires total biomass (the sum of aboveground and belowground).

Unfortunately, the belowground biomass is not included in the historical dataset. Previous studies conclude that the below-aboveground biomass ratio can be used to estimate the belowground biomass. However, this biomass ratio in the grassland varies among different vegetation types. The below-aboveground biomass ratio (b_a_ratio) of meadow steppe, typical steppe, and desert steppe in IMAR was found to be 7.04, 5.16, and 5.32, respectively60. These ratio metrics are used to estimate belowground biomass for different grassland biomes types in this study. In addition, grazing animals consumed considerable biomass for sites outside the protected area, which must be considered. There is no detailed multi-temporal data about locations with varied grazing intensity. The biomass consumed by grazing animals is estimated using the livestock statistics data from the yearly statistical yearbook of IMAR for the pastoral counties. The livestock statistical data is spatially re-allocated based on the area of the counties. The numbers of different types of livestock are converted uniformly to the standard sheep units based on the consumption of forage. Each sheep unit averagely consumes 1.8 kg dry forage per day according to the national standard of calculation of rangeland carrying capacity (NY/T 635-2015, Agriculture Ministry of China 2015). The total biomass (T_BIO) gap between with and without OLMPs can be written as,

$${{{{{\rm{T}}}}}}\_{{{{{\rm{BIO}}}}}}\_{{{{{\rm{gap}}}}}}=\,{{\max }}(0,{{{{{\rm{T}}}}}}\_{{{{{{\rm{BIO}}}}}}}_{{{{{{\rm{in}}}}}}}-{{{{{\rm{T}}}}}}\_{{{{{{\rm{BIO}}}}}}}_{{{{{{\rm{out}}}}}}})$$
(5)

where T_BIOin = (1 + b_a_ratio) × A_BIOin is the biomass density with OLMPs, and A_BIOin is the aboveground biomass. Similarly, T_BIOout = (1 + b_a_ratio) × A_BIOout + 1.8 × days × sheep_unit, where T_BIOout and A_BIOout are the biomass density and the aboveground biomass density outside the OLMPs implemented area, respectively, days is the accumulated grazing days starting from the date of vegetation green-up, which was set from May 1, to the date of the field data collection, August 31, and sheep_unit is the grazing intensity in the sheep unit outside the site.

The relative increase in vegetation productivity attributed to the implementation of OLMPs, is the ratio of the biomass gap (T_BIO_map) to the total biomass outside each site (T_BIOout, T_BIOout ≠ 0), which is formulated as,

$${{{{{\rm{Relative}}}}}}\_{{{{{\rm{BIO}}}}}}\_{{{{{\rm{gap}}}}}}={{{{{\rm{T}}}}}}\_{{{{{\rm{BIO}}}}}}\_{{{{{\rm{map}}}}}}/{{{{{\rm{T}}}}}}\_{{{{{{\rm{BIO}}}}}}}_{{{{{{\rm{out}}}}}}}\times 100 \%$$
(6)

where the computed Relative_BIO_gap indicates the possible increase of biomass when OLMPs get implemented. Similarly, the ratio of the carbon gap to NPP reflects the relative increase in NPP if the identified OLMPs are implemented at a location, which takes the form as,

$${{{{{\rm{Relative}}}}}}\_{{{{{\rm{Carbon}}}}}}\_{{{{{\rm{gap}}}}}}={{{{{\rm{Carbongap}}}}}}/{{{{{\rm{NPP}}}}}}\times 100 \%$$
(7)

A linear relationship between Relative_Carbon_gap and Relative_BIO_gap is computed to reflect their consistency. A moderate correlation between the estimated carbon gap and field observations was achieved, with R2 0.40 and a linear regression coefficient (β) 0.94 (Supplementary Fig. 11), which suggested good consistency between the estimated carbon gap and observed the increased potential of the grassland biomass.