Terrestrial ecosystems play an important role for the global carbon cycle as they act as substantial sinks and sources of carbon (C) . In both directions, fluxes in the land carbon cycle have significantly been altered in previous centuries due to anthropogenic land use and land cover changes (LULCCs), in particular through deforestation driven by early agricultural expansion in the mid-latitudes, recent tropical deforestation, and recent forest expansion in the mid- and high latitudes . Since 1850, the accumulated global net flux from LULCC (fLULCC) contributed approximately one-third of global anthropogenic CO2 emissions and was the dominant source until the 1950s, when fossil fuel emissions drastically increased . Despite its decreasing relative contribution, fLULCC comprises an important share of the global carbon budget (GCB) and might again account for the bulk of anthropogenic C emissions in the future, if fossil emissions can be drastically reduced as described in some socio-economic pathways . The fLULCC may also gain an important role in the quest for negative CO2 emissions technologies, with LULCCs such as reforestation and afforestation (denoted reforestation in the following) bearing significant potential to sequester atmospheric CO2 . Accordingly, fLULCC quantification is essential to better understand global carbon cycle dynamics, to estimate future climate change, and to support the assessment of greenhouse gas reduction efforts .

There is so far no general agreement on a single valid definition and approach to assess the fLULCC. This is because the fLULCC cannot be directly measured on a global scale due to the co-occurrence with natural C sinks and sources. For example, in managed forests, C fluxes result from logging and subsequent regrowth, which is part of the fLULCC, but also change in response to interannual variability or long-term trends in environmental conditions . Inventories or satellite-based measurements cannot distinguish C fluxes induced by LULCC from those induced by environmental changes. To separate these terms, models are applied. Here, various approaches exist. In the 2019 GCB of the Global Carbon Project (hereafter GCB2019; ), two bookkeeping models are used: “Bookkeeping of Land Use Emissions” (hereafter BLUE; ) and “Houghton and Nassikas 2017” (hereafter H&N2017; ). The bookkeeping mean fLULCC in the GCB2019 is combined with the uncertainty derived from process-based dynamic global vegetation models (DGVMs). DGVMs exist in much larger numbers and their process-based methods to calculate C fluxes allow one to account for the interplay of multiple drivers on C fluxes, which bookkeeping models cannot do.

However, estimates from bookkeeping models and DGVMs are not directly comparable due to underlying assumptions on C stocks . Bookkeeping models are semi-empirical models that combine observation-based C densities with information on areas affected by different types of LULCCs and response curves characterizing the speed of C uptake and release after specific LULCCs to calculate the fLULCC. In contrast, to isolate the LULCC effects from those of environmental changes, DGVM-based fLULCC is generally estimated as the difference of net land C uptake from net biome productivity (NBP) between simulations with and without LULCC. Within the GCB2019, these simulations are conducted under transient environmental conditions (such as climate, CO2 concentrations, and nitrogen deposition); therefore, synergistic fluxes between LULCCs and environmental changes are included.

The transient DGVM approach includes the loss of additional sink capacity (LASC), representing C fluxes in response to environmental changes on managed land (typically croplands with low C sink capacity and fast turnover rates) as compared to potential natural vegetation (typically forests with large C sink capacity and slower turnover rates; ). As an example, when an area that acted as C sink is deforested, the stored C is lost at harvest time corresponding to an instantaneous fLULCC. The resulting agricultural area typically does not constitute a major sink. In the simulation without LULCCs, the forest persists and may increase its C density over time, storing additional C in its slow-turnover woody and soil C pools in response to favourable environmental changes such as increased CO2 concentrations. Compared to the simulation without LULCC, the sink capacity would consequently be diminished in the simulation with LULCC. Thus, even though the instantaneous emissions of the deforestation event may have ceased, deforestation continues to alter the fLULCC since the reference simulation assumes the potential vegetation cover in the absence of LULCCs and simulates its response to environmental changes. This example illustrates an interesting aspect of the LASC: it has been acknowledged that the LASC in its literal sense (a loss of carbon, positive LASC values) is an unrealized C uptake potential and is not reflected in any real change in atmospheric CO2 concentration . However, as the LASC captures the foregone C sinks that were destroyed by a LULCC event (and likely accumulates even in absence of further LULCCs), it manifests in the budget of atmospheric CO2 as compared to a reference excluding LULCCs . In contrast to the theoretical nature of positive LASC values, negative values counted towards the LASC, for example due to reforestation, depict realized C uptake that is theoretically observable (though observations in the field are highly complex due to co-occurrence of natural carbon fluxes).

The result of a permanent reduction of a C sink on the LASC, as due to deforestation, is difficult to predict over time. Natural C sinks are subject to changes and can even turn into C sources for periods of time, due to the interplay of multiple factors that control the C balance of ecosystems simultaneously. For example, the LASC may increase because of an increased C uptake via higher NBP resulting from atmospheric CO2 increases (; or review of CO2 effect in ) or global-warming-induced longer growing seasons in northern latitudes and higher altitudes . Conversely, environmental driven decreases in C stock turnover times, for example due to an increased frequency and severity of drought and heat stress events or increased fire (included in some DGVMs of the GCB2019), may reduce NBP and thus may cause LASC decreases (and lower fLULCC estimates). The LASC will thus differ in magnitude and direction over time and across space.

Environmentally induced C stock changes not only alter the LASC, but also the instantaneous fLULCC. For example, the fLULCC from clearing pristine forest is expected to be higher today than during pre-industrial times if the forest has grown denser over time. Additionally, legacy effects result from the ongoing adaption of ecosystems to historical environmental changes . Such transient environmental effects are excluded in bookkeeping approaches – either through using constant C densities, or through purposefully excluding alterations in C densities from transient DGVM simulations in reduced-complexity Earth system models . The independence or dependence of vegetation and soil C densities from environmental conditions is thus another difference between transient DGVM and bookkeeping approaches. Here, DGVM simulations under constant environmental forcing can help to attribute fLULCC quantities independent of the timing of LULCCs.

DGVM simulations under constant environmental conditions have been performed within the project “Trends and drivers of the regional-scale sources and sinks of carbon dioxide” (TRENDY; ), when conducting the simulations for the GCB2019 . This included a first set of simulations that quantify the fLULCC based on constant present-day environmental conditions. This approach is more similar to bookkeeping estimates and can be evaluated against Earth observation or inventory data as it most closely represents the observable state under today's conditions and excludes transient flux alterations. Moreover, recent observations are commonly used to estimate the past, for example by combining observed C densities with vegetation coverage reconstructions to infer C stocks in human absence or with historical area changes for time series of C stock losses .

However, as fLULCC quantities derived under constant present-day conditions are independent of long-term environmental trends, the increased C stocks due to spinup with present-day environmental conditions may lead to comparably higher fLULCC estimates, especially in early simulation years (environmental changes during the industrial period, in general and on global scale, increased C stocks; refer to Fig.  for illustration). More realistic fLULCC estimates for the early period can be derived assuming that pre-industrial environmental conditions prevailed over time ; however, despite being based on the same land use dataset, this leads to comparably lower fLULCC estimates, in particular for later LULCCs .

Assuming constant environmental conditions or C densities over time is clearly unrealistic and requires an arbitrary decision on the time period to determine these variables' values. On the other hand, as discussed, the lost sinks in DGVM-based fLULCC under realistic, transient environmental conditions do not correspond to observable fluxes. This poses the question about a proper definition of fLULCC for a robust and realistic attribution that is valid across time and space. It needs to be decided whether the LASC should be included or excluded (as argued, e.g. in ) as part of the fLULCC and consequently be counted towards the terrestrial C sink or not. The urgent need to address this question is underlined by the fact that past LULCCs are estimated to have committed a reduction in the potential global C sink of 80–150 PgC by 2100, which depending on the scenario, translates into a share of ∼70 % of the total global fLULCC .

This study aims to strengthen the basis for a decision on how to define the fLULCC, in particular with respect to the ability of different approaches to resolve the LASC, and thus is a guide on the future role of DGVMs in fLULCC attribution. To this end, we present analyses concerning the relevance of different assumptions on environmental conditions, for which the recent extended set of TRENDY DGVM simulations was performed. In particular, our study (1) discusses and quantifies three DGVM-derived fLULCC (under pre-industrial, transient, and present-day environmental conditions) and bookkeeping estimates in conjunction with their inherent differences on global scale, (2) quantifies the temporal evolution of the differences in DGVM-derived fLULCC estimates for 18 regions, (3) differentiates between climate- and CO2-induced fLULCC components as derived by DGVMs, and (4) aims to approach a spatio-temporally homogenized attribution of the fLULCC as derived by models.

This study is based on an ensemble of TRENDY v8 models (http://sites.exeter.ac.uk/trendy/, last access: 5 April 2021) that ran simulations with and without LULCC for the period 1700–2018 (used in the GCB2019 to quantify the fLULCC uncertainty and to estimate the natural terrestrial C sink; ). It is ensured that all models have reached (1) a steady state after spinup (offset in global NBP < 0.1 PgC yr-1 and drift < 0.05 PgC yr-1 per century), (2) a net land flux over the 1990s within 90 % confidence of constraints by global atmospheric and oceanic observations, and (3) fLULCC as a C source to the atmosphere over the 1990s .

The previous sections have shown for the first time that fLULCC patterns depend not only on the timing of occurrence and type of LULCCs, but also on the simulated time period and the assumptions on environmental conditions (with spatially very diverse effects from climate alterations). From a policy standpoint and disregarding considerations from the natural land sink perspective, these results highlight the need for a fLULCC estimate that is comparable over time and across space. For example, including the LASC in fLULCC estimates may be perceived as appropriate because LULCCs could have destroyed or created vegetation with long C turnover (e.g. deforestation or reforestation) leading to decreased or increased C sinks (while current fLULCC reporting neglects such foregone sinks). However, including the LASC implies attributing fluxes to a region's emission budget that are partly a fate of history; particularly in the temperate regions, LULCCs detrimental to C stocks historically happened earlier compared to LULCCs increasing C stocks. Thus, the committed emissions included in the LASC often have longer accumulation periods for detrimental as compared to beneficial LULCCs whose accumulation periods are more likely to be cut off at the simulation end (2018 in the GCB2019). The accumulation periods may be further altered if, over the historic period, various LULCCs occurred on the same area. This is further complicated because environmental changes over the historic period modified the LASC with a widely accelerated accumulation rate in later periods due to higher and faster increasing CO2 concentrations but very heterogeneously spread alterations by climatic changes. Thus, even for the same LULCC with the same accumulation duration, the LASC will be different depending on the timing and location of the LULCC.

To circumvent these issues, as could be desired in the political context, one could derive fLULCC and the LASC based on simulations forced with the cycled climate and CO2 conditions that occurred during the actual LULCC event. However, this would still result in differing accumulation periods and varying environmental conditions during and following a LULCC event. While the influence of the latter could be reduced using cycled pre-industrial or present-day environmental forcings, these neglect transient C stock changes. To consider the LASC but counteract spatial heterogeneity in fLULCC differences resulting from synergistic effects of environmental conditions and the timing of LULCCs, one could derive the fLULCC and LASC from a defined reference period that is independent of the actual time that LULCCs occurred and shares the same reference conditions. For example, the fLULCC and LASC could always be modelled for the second half of the 21st century, as here the environmental C stock changes have been amplified due to the accelerating increase of atmospheric CO2 concentrations (alternative start times are of course conceivable). By using such a reference period, the LASC could also be fully captured for most recent LULCCs (regardless of whether they act positive or negative on C stocks) and foregone sinks would be more equally counted (same length of accumulation period with similar environmental changes). Along these lines, it may be considered to calculate such an adapted LASC based on CO2-only simulations as in this case the impact of humans is more homogeneously distributed, while the spatially heterogeneous climate impact on fLULCCs, determined foremost by action outside the location of LULCCs, causes a questionable attribution of the regional fLULCC when compared across the globe (without even considering externalized fLULCCs; e.g. due to remote market demand of food and timber; ). To detach fLULCC estimates from the timing of LULCCs and the spatially heterogeneous climate evolution, we argue to address the delineation of an adapted LASC in future studies, where, in particular, the reference to calculate the LASC should further be investigated. Such methodology could limit the fLULCC to locally determined factors (namely LULCCs) and reduce the dependence on the timing of LULCCs while still reflecting the foregone C sink capacity by human intervention.

Accurate quantification of the net carbon flux from land use and land cover changes (fLULCC) is essential, foremost to project carbon (C) cycle dynamics and estimate the strength of negative CO2 emission technologies. However, the fLULCC can only be estimated by models – typically bookkeeping or dynamic global vegetation models (DGVMs) – and requires decisions on how to account for the effects of environmental changes. We show that these decisions have major consequences for flux attribution, particularly at the regional scale because C stocks evolve very heterogeneously in both space and time. DGVM estimates under present-day environmental forcing most closely resembled bookkeeping estimates (used in the annual global carbon budgets, GCBs) and are generally higher compared to the fLULCC under pre-industrial environmental conditions. This environmental equilibrium difference (EED; accounting for ∼35 % of global fLULCC when using present-day C stocks) is caused by higher C stocks, mainly in response to increased present-day atmospheric CO2 and only to a smaller extent by climatic changes. The EED becomes negative in some regions, mainly due to environmental conditions decreasing C stocks (e.g. increased frequency and intensity of droughts and reduced precipitation). In the GCB, cumulative bookkeeping fLULCC estimates are jointly published with DGVM-derived uncertainties under transient environmental conditions, which we show implies pronounced regional differences (named “present-day” vs. “transient” environmental conditions difference; PTD), strongly depending on the timing and placement of land use and land cover changes. We explain PTD values mainly by the loss of additional sink capacity (LASC), emissions due to destroyed C uptake potential that are only captured by the transient DGVM approach. In our multi-model mean for 2009–2018, a LASC of 0.8±0.3 PgC yr-1 accounts for ∼40 % of recent global fLULCC estimates of 2.0±0.6 PgC yr-1 (under transient conditions).

The LASC causes regionally strongly increased transient fLULCC (>0.1 PgC yr-1) where LULCCs detrimental to C stocks, such as deforestation, happened early within the simulated period (long accumulation period for lost potential C uptake; foremost in the USA) or later on areas with strong positive C stock response to environmental changes (e.g. in Brazil, Southeast Asia, and equatorial Africa). The LASC from deforestation is unaccounted for in nations that deforested prior to the beginning of the accounting period (e.g. widespread deforestation in Europe). Further, in many of these cases the LASC is negative and transient fLULCC is strongly decreased due to early reforestation on previously deforested land where re-established forest carbon stocks profited from environmental change (e.g. widespread in Europe). Within the political context, if environmental effects on C sink capacity are to be accounted for in regional budgets (requiring DGVMs for the assessment) we argue for a consistent method that includes the LASC and emphasize that care must be taken in choosing the beginning of the accounting period. As LASC values derived by the approach taken so far in the GCB are widely independent of locally determined environmental changes (rather, they depend on globally determined climatic changes) and strongly dependent on accumulation periods (defined by the timing of LULCCs and the end year of the simulations), we argue for a fLULCC attribution that is more robust against choices of environmental drivers and accumulation period by using an adapted LASC, for example, based on a defined common reference period and homogeneously altered environmental conditions (such as only being driven by CO2 alterations).