Anthropogenic emissions of CO2 are the main driver for observed climate change and primarily result from the combustion of fossil fuels and anthropogenic land use and land use change (LUC) . Conceptually, fossil fuel emissions can be regarded as an external forcing acting upon the C cycle-climate system. In contrast, LUC additionally modifies the response of terrestrial ecosystems to elevated CO2 and changes in climate and thereby affects the C cycle-climate feedback . This leaves room for interpretations as to how exactly land use change emissions (eLUC) are to be defined and where the system boundaries are to be drawn.

The definition of eLUC is relevant for the accounting of the global C budget . Top-down derived land-atmosphere C fluxes that are not explained by bottom-up estimates of eLUC are commonly ascribed to the residual terrestrial C sink. Differences in the definition of eLUC thus directly translate into differences in estimates for the residual terrestrial C sink. This budget term is a major source of uncertainty in climate projections and its quantitative understanding motivates a large part of current research in biogeochemistry and terrestrial ecology.

Common to almost all approaches to quantify “CO2 emissions from land use change” using global process-based models, is that eLUC is calculated as the difference in the global total land-to-atmosphere flux (F) between a realistic world where land vegetation cover and C pools are affected by prescribed, time-varying LUC maps (subscript LUC) and a hypothetical world, where no LUC is occurring (subscript 0): eLUC=FLUC-F0. However, the definition or model setup, under which FLUC and F0 are calculated, is relevant as it implies the inclusion of secondary fluxes. (henceforth termed SM08) laid out a framework to distinguish between different component fluxes arising from land use, including primary emissions from converted land, and secondary emissions arising from the interactions between climate, CO2 and LUC. (henceforth termed PG14) show that numerous different definitions of eLUC have been used in the published literature, implying a bewildering array of different combinations of component fluxes that are counted towards eLUC in the different studies. SM08 and PG14 demonstrate conceptually that due to this, typical eLUC estimates derived from observation-driven bookkeeping models, offline Dynamic Global Vegetation Models, and coupled Earth System Models give systematically different results.

Substantial, setup-related differences in eLUC estimates have been found in earlier studies , and different component fluxes have been identified and quantitatively separated within their respective modelling framework . SM08 distinguished between primary emissions that capture the direct effects of land conversion, and secondary effects arising from the interaction of land conversion and environmental change (CO2 and climate). SM08 further separated the secondary fluxes into the land use feedback flux and the replaced sinks/sources flux. We term these eLFB and eRSS, respectively, and provide definitions in Sect.  and quantifications in Sect. . Recently,  (GC13) provided quantitative estimates of historical eLUC following different definitions. However, their analysis is limited to offline vegetation model quantifications and thus cannot address the aforementioned discrepancies between offline and ESM methods.

Here, we apply a single model, use a simple formalistic description of eLUC flux components inspired by GC13 and SM08, and follow the classification of PG14 to distinguish different methods of eLUC quantification. We quantify these differences for the historical period and a future business-as-usual scenario (RCP8.5). In contrast to earlier studies , we designed model setups to limit differences in eLUC to merely conceptual ones by using climate and CO2 outputs from the coupled simulations to drive offline simulations, instead of using observational data for the latter. We will demonstrate that such definition differences imply inconsistencies of estimated land use emissions on the order of 20 % on the global scale and may increase to 30 % under a future business-as-usual scenario. This is directly relevant for territorial C balance accounting and national greenhouse gas balances under the Kyoto Protocol and thus inherently carries a political relevance.

We elucidate the implications of the choice of definition for the residual terrestrial C sink and global C budget accounting and discuss how eLUC quantifications may most appropriately be defined in studies that rely on multiple methodological approaches. In such cases, we propose, following , to resort to the “least common denominator”, following the bookkeeping approach (method D1 in PG14), where LUC emissions are defined without accounting for any indirect effects on terrestrial C storage caused by transient changes in CO2 or climate.

We start by revisiting the classification of PG14 for a subset of eLUC quantification methods identified in their study. We focus our analysis on the discrepancy between eLUC derived from bookkeeping and offline vegetation models (D1 and D3 methods) and coupled ESMs (E2 method). Results of the D3 method feature prominently in model intercomparison studies , the Global Carbon Project and the IPCC , and are often presented along with and compared against D1-type estimates. Yet, a consistent separation of commonly identified component fluxes can only be achieved by ESMs (see below).

SM08, PG14, and GC13 establish a formalism to describe and discuss the different definitions of total eLUC and its component fluxes. Here, we synthesize these previous frameworks to a minimal description that allows us to identify the different flux components contained in eLUC provided by the offline DGVM setups (D3 method), coupled ESM model setups (E2  method), and the bookkeeping approach (D1 method). We then show that eLUCE2 = eLUC0 + eRSS + eLFB plus synergy terms. We propose a definition for the delineation between component fluxes that follows a separation along underlying drivers of environmental changes, and that allows a consistent identification of component fluxes in coupled model setups with and without the FF forcing. The formalism presented below sets the basis for the analysis and discussion in subsequent sections.

A reference time (or period) t0 is selected. At t0 all land with total area A0 is “undisturbed” with respect to land use changes that take place after t0. The reference area A0 may include agricultural land that was converted before t0. Net atmosphere-land carbon fluxes at t0 and thereafter may not vanish as the land system may not be in equilibrium with the atmosphere. Under commonly used model setups, the extent of agricultural land in the reference state is small in comparison to the area under natural vegetation. Similarly, models are typically spun-up towards equilibrium and remaining trends in atmosphere-land fluxes are small. For simplicity, we neglect these disequilibrium fluxes below.

Additional fluxes arise due to forcings that occur after the reference time. We separate forcings into a land use change (LUC) and a non-land use change component (FF) such as fossil fuel emissions, nitrogen deposition, ozone changes etc. In a simulation without LUC, these additional fluxes occur on undisturbed land (subscript “und”) and are caused by FF (use of superscript analogous as in Eqs.  and ) and we write F0FF(t) = A0ΔfundFF(t). Δ denotes a change in a variable relative to the reference time t0 (e.g. Δf(t) = f(t) - f(t0)). Note that fFF(t0) is zero by definition. Below, we drop the specification of t. In a simulation with LUC, we can write fluxes occurring over land that has not been converted since the reference time t0 (subscript “und”) and land that has been converted after t0 (subscript “dis”) as FLUCFF+LUC=A0-ΔAΔfundFF+LUC︸undisturbed land+ΔAf0+ΔfdisFF+LUC︸disturbed land. ΔA is the total area that has been converted, e.g. from natural to cropland or vice versa, since the reference time and up to the point in time of interest. Note that disturbed and undisturbed land both “see” the environmental forcing caused by FF and LUC. GC13 treat fluxes on disturbed land as a vector representing land area cohorts that have transitioned from natural to agricultural land at a given time. Here, we drop the vector notation for individual age cohorts after conversion and lump these into a scalar representing non-natural (agricultural) land of varying age (ΔA(f0 + ΔfdisFF+LUC)). f0 are direct emissions in response to land conversion under constant environmental conditions and comprise instantaneous and legacy fluxes due to LUC after t0 as identified by Iu and Lu in PG14; ΔfdisFF+LUC is its modification due to environmental change (δI and δL in PG14). Note that on long timescales, the cumulative flux of (ΔfdisFF+LUC) is independent of the magnitude of f0.

Using Eq. () and ΔfFF+LUC = ΔfFF + ΔfLUC + δ allows us to expand and re-arrange terms in Eq. () and to write the total C flux induced by LUC after t0 as a sum of commonly separated component flux components, primary emissions (eLUCo), replaced sinks/sources (eRSS), and the land use feedback flux (eLFB) plus synergy terms: eLUCE2=FLUCFF+LUC-F0FF=ΔAΔfdisFF-ΔfundFF(eRSS)+A0-ΔAΔfundLUC+ΔAΔfdisLUC(eLFB)+ΔAf0eLUC0+A0-ΔAδund+ΔAδdis(synergy). We emphasize that eLUC includes only those fluxes due to land conversion after the reference time. Any legacy fluxes from land conversion before t0 are not included. Atmosphere-land fluxes arising from a disequilibrium at t0 affect FLUCFF+LUC and F0FF and thus cancel, apart from synergy terms. A0ΔfundFF is the land-atmosphere flux in a simulation forced only by FF and can be interpreted as the potential land C sink (ePS) under environmental change caused by FF. ePS=A0ΔfundFF. The above definition (Eqs. 6–10) of the total C flux induced by LUC corresponds to the E2 method, eLUCE2 (Eq. ). eLUC0 are primary emissions and equivalent to eLUCD1, as quantified using a bookkeeping approach. Analogously, component fluxes of the land-atmosphere CO2 exchange in the different model setups Fik can now be identified (see Table ).

In spite of the variety of terminologies presented in the published literature, studies generally agree that total C fluxes induced by LUC can be split into primary emissions, eLUCo, that capture the direct effects of land conversion, and secondary effects arising from the interaction of land conversion and environmental change (CO2, climate). However, the exact delineation between secondary emissions eLFB and eRSS differs . Here, we chose a definition so that eRSS arises due to environmental changes (e.g. CO2 , climate, N-deposition, ozone, air pollution, etc.) that are not caused by LUC, whereas eLFB is due to environmental changes driven by LUC. According to Eq. (8) and for a reference state without land under use, eRSS can be interpreted as the difference in sources/sinks between land under potential natural vegetation (ΔfundFF) and agricultural land (ΔfdisFF) and scales with the area of land converted ΔA. The LUC-feedback flux eLFB (Eq. 9) describes the flux arising as a consequence of LUC-induced environmental changes (e.g. CO2, climate change). eLFB occurs on non-converted (natural) and converted (agricultural) land, with different sink strength (ΔfundLUC and ΔfdisLUC). To sum up, eRSS arises from secondary effects of fossil fuel emissions (and N deposition, etc.), whereas eLFB is driven only by LUC. This is reflected by the fact that only superscript “LUC” occurs in the definition of eLFB, whereas only “FF” occurs in the definition of eRSS. The definitions of eRSS, and hence of eLFB differ slightly between publications . SM08 defined eLFB so that this flux only occurs on remaining natural land. Specifically, the term (ΔAΔfdisLUC) appears in eLFB here, while it is ascribed to eRSS in SM08. However, this flux component is relatively small (see Fig. ). As indicated by PG14, eRSS may also be defined as eRSS = ΔA(ΔfdisFF+LUC - ΔfundFF+LUC), implying that eLFB = A0ΔfundLUC. Our choice of eRSS and eLFB has the advantage that it follows an intuitive separation between underlying environmental drivers (FF vs. LUC) and that eLFB can identically be separated in coupled ESM-type simulations where the FF forcings are excluded. This corresponds to the E1 definition in PG14, with eLUCE1 = FLUCLUC - F00 = eLUC0 + eLFB, and was applied by and .

For clarity, we have dropped the temporal and spatial dimensions of fluxes and areas and have reduced the formalism to a distinction only between undisturbed and disturbed (converted) after the reference time t0. This is a simplification for a formal illustration and we note that the simulations presented in Sect.  account for the full complexity of fluxes across space, different agricultural and natural vegetation types, and time.

As pointed out in earlier publications by SM08, PG14, and , as well as in Sect. , eLUCdIII and eLUCeII are not identical and hence eLUCdIII cannot be written as the sum of component fluxes identified above. In other words, while primary emissions eLUCo can be consistently derived from offline DGVMs by simply holding environmental conditions constant, the secondary fluxes derived from such studies are neither equal to eRSS, nor eLFB, nor the sum of the two. In other words, eRSS and eLFB cannot be separated as shown here using offline vegetation models. eLUCD3-eLUC0≠eRSS+eLFB. By expanding terms analogously to above derivation, the difference between eLUC quantifications from the E2 and the D3 methods turns out to be eLUCE2-eLUCD3=A0ΔfundLUC+δund. Ignoring the synergy term δund, the discrepancy can thus be interpreted as a flux, triggered by environmental changes caused by LUC, but occurring on land not converted since the reference period (ΔfundLUC). Note that this is not identical to eLFB as defined here. The same theoretical result can be found when applying the formalism of PG14 and their definition of flux components in eLUCeII and eLUCdIII, with the difference turning out to be (δl + σl,f)(En + Ep).

In the literature, eLUC estimates from bookkeeping (corresponding to D1) and offline vegetation models following the D3 method are often presented alongside . Conceptually, they are not identical and estimates thus imply systematic differences. We can analogously decompose the fluxes in each simulation (see also Table ) and write this difference as eLUCD3-eLUCD1=eRSS+ΔAΔfdisLUC-ΔfundLUC+ΔAδdis-δund. Note that the term ΔA(ΔfdisLUC - ΔfundLUC) is sometimes included in eRSS implying that the difference between D3 and D1 is described simply by eRSS. However, our definition of eRSS differs.

In order to quantify the individual flux components and the discrepancy between the different quantifications of eLUC outlined in previous sections, we apply the emission-driven, coupled Bern3D-LPX Earth System Model of Intermediate Complexity as described in and the offline DGVM model setup where the LPX DGVM is driven in an offline mode as described in . Results from the offline vegetation model were also used in global C budget accountings , following the D3 method for estimating eLUC therein. The model is spun up at constant boundary conditions representing year 1700 (CO2 insolation, HYDE-based, land use distribution from the LUH data set , and recycled 1901–1931 CRU TS 2.1 climate ). Model drift is absent after the spin-up. During the transient simulation (1700–2100), climate is simulated by adding an anomaly pattern, scaled by global mean temperature change relative to 1700, to the continuously recycled CRU climatology (temperature, precipitation, cloud cover). This implies that unforced variability is identical in all simulations. We focus on results after 1800 but chose an early start of the transient simulation (1700) in order to minimise effects of the initial equilibrium assumption for LUC-related fluxes. For the historical period and the future “business-as-usual” scenario (RCP8.5), we apply CMIP5 standard inputs . Land use change is simulated following the Generated Transitions Method, including shifting cultivation-type agriculture and wood harvesting, as described in . In contrast to the previous studies by and , we apply the model at a coarser spatial resolution (2.5∘ × 3.75∘, instead of 1∘ × 1∘). This has negligible effects (see Sect. ). LUC-related CO2 emissions are calculated as the difference in the land-atmosphere CO2 exchange flux between the simulation with and without LUC using Eq. () for the bookkeeping, Eq. () for the coupled, and Eq. () for the offline setup. In the coupled ESM setup, atmospheric CO2 concentrations and climate evolve interactively in response to the respective forcings. In the offline model setup following the D3 method, we directly prescribe climate fields and CO2 concentrations to the vegetation component (LPX model). In this case, climate and CO2 are taken from the output of the coupled ESM simulation, driven by FF and LUC (FLUCFF+LUC) and are prescribed to both offline simulations, with and without LUC. This corresponds conceptually to the common setup chosen for D3-type simulations, but instead of prescribing CO2 and climate from observations (which is the result of FF and LUC as well), we prescribe it from the coupled model output here in order to exclude differences in forcings between the coupled (E2) and offline (D3) setups, and to focus on differences in computed emissions implied by the different definitions.

The model is run in a set of simulations (see Table ) that allows us to disentangle flux components eRSS and eLFB and to assess the additivity assumption (ΔfFF+LUC = ΔfFF + ΔfLUC + δ). Using the description of decomposed fluxes given in Table  and the definition of eRSS in Eq. (7), the replaced sinks/sources flux component can be derived from simulations described in Table  as eRSS=FLUCFF+LUC-FLUCLUC-F0FF+A0-ΔAδund+ΔAδdis. Again, we may ignore the synergy terms δ. The expression of Eq. () also follows intuition. It represents the flux induced by environmental conditions caused by fossil fuel emissions in a world with LUC (FLUCFF+LUC - FLUCLUC) and a world without LUC (F0FF - F00). The last term is zero, except for unforced variability, as neither LUC nor changing environmental conditions are acting. Alternatively, eRSS can also be derived as (FLUCFF+LUC - F0FF+LUC) - (FLUCLUC - F0LUC), which is formally identical to Eq. (), assuming additivity of the FF and LUC forcings. Analogously, the land use feedback flux can be derived as eLFB=FLUCLUC-FLUC0. Also this can be understood intuitively. eLFB represents the total land-atmosphere flux in a world with LUC (but without fossil fuel emissions), FLUCLUC, minus the direct effects of LUC, FLUC0. In other words, it represents the secondary flux caused by LUC alone. Again, alternatively eLFB can be derived as FLUCFF+LUC - FLUCFF, which is identical to Eq. (), except for synergy effects.

Figure  reveals that global fluxes due to FF and due to LUC forcing alone combine in an almost perfectly additive fashion to the flux induced by the combined effect of FF and LUC up to present and discernible deviations (δ) emerge only in a future scenario of continuously rising CO2 and changing climate and contribute ∼ 10–20 % by 2100 in RCP8.5. This confirms the validity of the additivity assumption (ΔfFF+LUC = ΔfFF + ΔfLUC + δ) that underpins the flux component decomposition in Sect. .

Figure  illustrates annual emissions from LUC as quantified from the different approaches. During the historical period, the offline quantification (D3) suggests ∼ 23 % higher emissions than the coupled setup (E2). Cumulative emissions amount to 164 GtC with D3 and 133 GtC with E2 (AD 1850–2005, see Table ). SM08 applied observational CO2 and climate in simulations used for D3. They found slightly higher differences of D3 vs. E2 (30 % higher in their D3). report a difference of ∼ 100 % for a case where they only used CO2 concentrations from their interactive FLUCFF+LUC to force their F0FF+LUC simulation. A stronger effect in this case appears plausible as the replaced sinks/sources flux due to climate and CO2 effects are generally opposing . applied the same model at a 1∘ × 1∘ resolution following the D3 and D1 methods to quantify “total” and “primary” LUC emissions. Results at the finer resolution (165 GtC for “total GNT” in their Table 3) are virtually identical to the present estimate. The bookkeeping method yields cumulative historical fluxes of 152 and 177 GtC under preindustrial and present-day environmental conditions. Primary emissions under preindustrial and present-day background exhibit largely identical temporal trends but differ in absolute magnitude. 16 % higher emissions under present-day conditions are due to generally larger C density in natural (non-cropland and non-pasture) vegetation and soils simulated under elevated CO2 (364 ppm) and the warmer climate (corresponding to years AD 1982–2012 in the CRU TS 3.21 data set ). Differences in constant environmental conditions thus have qualitatively the same effect as uncertainty in C stocks on natural and agricultural land. I.e. eLUCdI scales linearly with simulated differences in natural and agricultural land and the trends in eLUCdI derived under preindustrial and present-day environmental conditions are identical, but markedly different from trends in eLUCdIII and eLUCeII.

Cumulative historical emissions following the D1 method under preindustrial (present-day) conditions are 14 % (33 %) higher than suggested by the E2 method. These differences are substantial and are on the order of the model range as presented in intercomparison studies or on the order of effects of accounting for wood harvest and shifting cultivation . For the future period (AD 2006–2099) following RCP8.5, cumulative emissions (2004–2099) for the D3 and E2 method are on the same order (192 and 188 GtC), but considerably higher than for the D1 method (133 and 153 GtC under preindustrial and present-day conditions). Differences with respect to the relative increase from present-day emission levels (average over 1995–2004) to projected levels in the last decade of the 21st century are even larger. Following the D1 method, the increase is 22 % (34 %) when holding conditions constant at preindustrial (present-day) levels. Due to different inclusion of secondary fluxes, the projected increase following the D3 method is 67 and 121 % following E2.

Figure  illustrates the different flux components of total emissions from LUC following the E2 method and reveals the underpinnings of the discrepant levels and trends of emissions when quantified with different methods. During the historical period (AD 1850–2005), eRSS cumulatively adds 6 % to primary emissions, similar as in SM08 (5 %), while eLFB reduces them by 17 %, similar as in SM08 (18 %) but less than in and (30–40 %). At present, eRSS and eLFB are of similar magnitude, hence total (eLUCeII) and primary emissions (eLUCo) are at approximately the same level. In RCP8.5, atmospheric CO2 and temperatures continue to grow, while land conversion rates and primary emissions are stabilised. As a result eLFB is stabilised, while eRSS continues to increase and contributes ∼ 50 % to total emissions in 2100. This explains the different trends in “total” (based on E2 and D3) versus primary emissions.

The difference between eLUCeII and eLUCdIII is of approximately the same magnitude as eLFB , although slightly smaller, and exhibits a trend that is closely matched by eLFB until roughly AD 2030 (see dashed line in Fig. ). This is expected as the difference, derived in Eq. (), is equal to A0(ΔfundLUC + δund), and thus resembles the definition of eLFB (see Eq. 8).

Secondary emissions are determined by the magnitude of C sinks and sources induced by environmental change, occurring differently on disturbed (agricultural) and undisturbed (natural) land. Figure  reveals that the C sink capacity on natural land under rising CO2 and a changing climate (year 2100, RCP8.5) is greatest in semi-arid regions of the Tropics and Subtropics and along the boreal treeline. In contrast, agricultural land at low latitudes acts as a net C source under environmental change and a net sink at high latitudes. The difference between the sink strength on natural and agricultural land is related to the eRSS component flux and reveals that the Tropics are the most efficient potential C sinks. Interestingly, at high latitudes, agricultural vegetation is an even more efficient C sink than natural vegetation. Figure  also provides information about the spatial distribution of synergy effects from the combination of the FF and LUC forcings, corresponding to the differences between the red and the black curves in Fig.  in year 2100. The sum of individual effects is greater than their combination in almost all vegetated areas, but most pronounced along the transition zone between forest and open woodland. Opposite effects are simulated in individual gridcells and are likely related to the threshold-behaviour of the dominant vegetation type.

To quantify the differences in eLUC quantifications by coupled ESM (E2 method), offline DGVMs (D3 method), and the bookkeeping method (D1 method), we applied a model setup where differences stemming from driving data are removed. Then, discrepancies in total eLUC arise exclusively from the applied methods (D1, D3, E2). Our results suggest that such discrepancies in global eLUC estimates are substantial for the historical period and imply strikingly different trends in eLUC for a future business-as-usual scenario. These differences stem from the implicit inclusion of secondary flux components. As we have pointed out, secondary fluxes derived from offline vegetation model setups are conceptually not identical to what is commonly referred to as the replaced sinks/sources flux or the land use feedback, nor the sum of the two.

Land use change is a substantial driver of the observed CO2 increase and has contributed about 25 % to total anthropogenic CO2 emissions for the period 1870–2014 . Current (2004–2013) emission levels are 0.9 ± 0.5 GtC yr-1 . Reducing emissions from deforestation and forest degradation is now an important part of international climate change mitigation efforts under the United Nation Framework Convention on Climate Change. Periodically issued synthesis reports by the IPCC , annually updated CO2 flux quantifications by the Global Carbon Project , as well as multi-model intercomparison projects provide valuable information on LUC CO2 emissions. However, values derived from different approaches are commonly presented alongside and respective uncertainty ranges partly stem from implicit methodological differences. The lack of a standard methodological protocol for LUC emission estimates and the inclusion of secondary fluxes also obscures the scientific interpretation of model results and their comparison with observational data. Below, we outline two different perspectives on what “emissions from LUC” may represent.

Estimates of CO2 emissions from land use are essential to quantify the global C budget and inform climate change mitigation policy. However, inconsistent methodologies have been applied in syntheses based on multiple models and methods. In order to guarantee comparability and continuity, we recommend that modelling studies provide estimates derived under constant, preindustrial boundary conditions (D1 method). This method can be followed by offline vegetation models and Earth System Models, and is best comparable to observation-based estimates following the bookkeeping approach. This implies that the residual terrestrial sink derived from the global C budget includes the sink flux stimulated by environmental changes in response to LUC and reflects effects of replacement of potential C sinks due to land conversion. We have suggested how coupled, emission-driven Earth System Models may be applied to separate component fluxes defined here. Such analyses are essential to capture the full impact of LUC on climate and CO2.