The starting point for this step is the potential distribution of C plantations around the world. Six plantations types were selected on the basis of the 'Top 14 Most Planted World's Trees' 2848 to represent suitable species in different climatic zones around the world (Table 5). We used, for example, gum species (Eucalyptus spp.) for the tropical regions, and spruce (Picea abies) and larch (Larix kaempferi) for plantations in cool and boreal regions, respectively. 'Potential distribution' in this context refers to the availability and suitability of land. Land is assumed to be available when it is not assigned as protected area and no longer used for agriculture (neither cropland nor pasture). Hence, a more realistic potential is provided, given the many other land-use purposes that may expand in the (short-term) future. Suitability of land is driven by various environmental conditions in terms of climate and soil. All these conditions need to be fulfilled to allow a specific plantation type in a certain region. The climatic characteristics of the plantations are derived from the best matching Plant Functional Types (PFT) – classes of plant species grouped according to physiological characteristics and the sensitivity to changes in temperature and water availability (Table 5).

Secondly, the best growing plantations out of these six types are determined for each grid cell by using the parameters describing the C dynamics (e.g. lifetimes, allocation fractions). These parameters of the different plantation types are linked to the parameters used for the natural land-cover type that best matches the plantation type considered (Tables 5 &6; 4919). The Net Primary Production (NPPCP_ts) rates averaged over the longest likely rotation length (LRL) of each plantation type (Equation 1) are compared. The longest LRL has been chosen to take into account the period needed to reach the maximum NPP for all possible plantation types.

NPPCP_ts(t) = RF(t)·FNPP_lct(ts)(t)·AGF_ts

where

ts Index for tree species in a carbon plantation (1,..,6)

lct(ts) Land cover type by which the carbon dynamics of tree species (ts) are described (Table 1)

RF(t) Reduction Factor (≤1) during the period towards maximum average growth in terms of NPP, i.e. the recovery time (-) (Table 1)

FNPP_lct(ts)(t) NPP of full-grown natural vegetation in year t if the grid cell were to be covered by land-cover type lct(ts), as computed by the IMAGE 2 C cycle model (Mg C ha-1 yr-1)

AGF_ts Additional Growth Factor of tree species ts (-), (Table 1, Equation 2)

The additional growth factor (AGF_ts, Equation 2) is defined as the growth rate of a plantation – based on a literature review (Equation 3) – compared to the average growth of the natural land-cover type, corrected for historical environmental changes – CF95_ts. The latter correction factor is needed because the information taken from the literature on the NPP of plantations comprised, in general, data from around 1995. Following the rules in the Kyoto Protocol – stating that sequestration credits should only be based on 'direct human activities' – the NPP data needed to be adjusted. This is because these data include a growth stimulus caused by, among other factors, increasing CO₂ concentrations (which form 'indirect human activities'). The CF95 value for each plantation type (Table 5) has been derived by applying the IMAGE-2 C-cycle model in order to define the growth stimulants from CO₂ and climate since 1970. Note that we correct the sequestration potential up to 2100 in a similar way:

A G F t s = F N P P C P , t s N P P I l c t ( t s ) ⋅ C F 95 t s MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemyqaeKaem4raCKaemOray0aaSbaaSqaaiabdsha0jabdohaZbqabaGccqGH9aqpjuaGdaWcaaqaaiabdAeagjabd6eaojabdcfaqjabdcfaqnaaBaaabaGaem4qamKaemiuaaLaeiilaWIaemiDaqNaem4CamhabeaaaeaacqWGobGtcqWGqbaucqWGqbaucqWGjbqsdaWgaaqaaiabdYgaSjabdogaJjabdsha0jabcIcaOiabdsha0jabdohaZjabcMcaPaqabaGaeyyXICTaem4qamKaemOrayKaeGyoaKJaeGynauZaaSbaaeaacqWG0baDcqWGZbWCaeqaaaaaaaa@5586@

where

FNPP_CP,ts Average NPP of full grown plantations (Mg C ha-1 yr-1) around 1995 (Eq. 3)

NPPI_lct(ts) Average NPP of all grid cells in 1970 covered by land-cover type lct(ts) (Mg C ha-1 yr-1) 19

CF95_ts Correction Factor for climate-induced growth stimulants for 1970–1995 (-).

FNPP_CP can be derived from especially literature on plantations yields (2728345051 and Table 6). This information is subsequently used in Equation 3 (see also 19)

F = ( A S L S − A B L B ) + ( 0.5 − 2 A S L S − 2 A B L B ) F N P P C P = Y L D ⋅ W D ⋅ C F ⋅ L R L H I F ⋅ ( L R L − Re ⁡ cov ⁡ 2 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=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@7BEB@

where

AS Allocation Fraction of Stems (= 0.3)

LS Lifetime of stems, based on the underlying land-cover types lct(ts) (yr)

AB Allocation Fraction of Branches (= 0.2)

LB Lifetime of branches, based on the underlying land-cover types lct(ts) (yr)

YLD Yield of a plantation averaged over a rotation (m³ Fresh Volume ha^-1 yr^-1); (Table 7)

WD Wood density (Mg dry matter.m^-3 fresh volume; see Table 1)

HI Average harvest index or the fraction of above-ground biomass used (Table 1) of which the remainder decomposes to humus (-)

CF Average carbon factor or carbon content (Mg C m^-3 dry matter)

Recov Recovery time or the average time for a carbon plantation to reach maturity in terms of NPP (yr) (Table 6).

The last part in determining the physical potential (step 1) is to estimate the net C sequestration (CSeq) potential of the best growing species in a grid cell. This calculation is based on the concept of SPP (Surplus Potential Productivity), as introduced by Onigkeit et al. 52. The basic philosophy is to account only for the net C uptake of a plantation (Equation 4). This is calculated by using emissions associated with the conversion from natural land cover into a plantation and comparing the NEP flux of a plantation with the NEP flux of the natural vegetation that would otherwise grow in the area. As such, CSeq determines the additionality compared to the situation of having no plantations. Note that a negative value of CSeq corresponds to a biospheric uptake of carbon from the atmosphere. In our application, the NEP fluxes are simulated by the terrestrial C cycle model of IMAGE 2, taking into account NPP and soil respiration (see below).

C S e q = b ⋅ E + ∑ t = t 0 t = 2100 [ N E P ( t ) − N E P C P ( t ) ] MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaem4qamKaem4uamLaemyzauMaemyCaeNaeyypa0JaemOyaiMaeyyXICTaemyrauKaey4kaSYaaabmaeaacqGGBbWwcqWGobGtcqWGfbqrcqWGqbaucqGGOaakcqWG0baDcqGGPaqkcqGHsislcqWGobGtcqWGfbqrcqWGqbaudaWgaaWcbaGaem4qamKaemiuaafabeaakiabcIcaOiabdsha0jabcMcaPiabc2faDbWcbaGaemiDaqNaeyypa0JaemiDaqhddaWgaaqaaiabicdaWaqabaaaleaacqWG0baDcqGH9aqpcqaIYaGmcqaIXaqmcqaIWaamcqaIWaama0GaeyyeIuoaaaa@57D9@

where

CSeq Net carbon sequestration in a grid cell in the period t0 through 2100 (Mg C ha^-1)

t Year (between 2000 and 2100)

t0 Starting year of carbon plantations in a grid cell

NEP_CP(t) Net Ecosystem Productivity of best growing tree species in a grid cell (Mg C ha^-1 yr^-1)

NEP(t) NEP of the original vegetation according to the baseline scenario (Mg C ha^-1 yr^-1)

E C content of natural vegetation before the conversion into a carbon plantation (Mg C ha^-1)

b Burn factor of the initial harvest [either 0 or 1] (-)

The variables E and b account for carbon emissions related to the establishment of a carbon plantation. For plantations established on abandoned agricultural land, grassland or forest land just being logged, there is no clearing needed and 'b' is close to zero. When, however, an existing natural forest or woodland is converted into a carbon plantation, the original vegetation is assumed to be burnt entirely (i.e. b = 1), resulting in instantaneous emissions of carbon into the atmosphere. These emissions must first be compensated before a plantation is effective in mitigating the CO₂ build-up in the atmosphere.

Since management can have a considerable effect on the carbon uptake potential of plantations 5354, we included two possible harvest regimes. Either plantations are harvested at regular intervals or no harvest takes place at all. In the latter case, a plantation will grow to a stable level of carbon storage and a low additional C sequestration further in time in the soil. In the former case, a plantation is harvested at the moment of maximum C sequestration, (i.e. the NEP of a plantation averaged over the stand age starts to decrease), followed by re-growth. In our assessment the harvested wood from stems and branches is used to fulfill the wood demand. Leaves, roots and the non-harvested stems and branches enter the litter and humus carbon pools in the soil. The approach of displacing wood demand amounts to a displacement factor of 1 (assuming no leakage, i.e. no change in the wood sector).

Figure 5 illustrates step 1, showing the C dynamics of a Pinus radiata plantation on either abandoned agriculture or replacing a natural forest. In the case of establishing this plantation on abandoned agricultural land, the NPP of both the plantation and the natural forest – that would otherwise grow in the area – increases from zero up to the maximum value within the predefined recovery period. If responses to changing atmospheric CO₂ levels and climate are excluded, the NPP values will remain constant at the maximum value. The soil respiration of both the plantation and natural forest first decline because the carbon input from young trees is limited, whereas the decomposition rate starts at the much higher equilibrium level with respect to the previous (in this case agricultural) vegetation. After a period of decline, the respiration flux increases, since the soil carbon pools are filled up again. The respiration flux increases until it exceeds NPP. If the net carbon uptake of the carbon plantation [NEPCP(t)] is larger than the net uptake of the natural forest [NEP(t)] (i.e. more negative), the plantation is effective in slowing down the build-up of atmospheric CO₂. This is illustrated by negative values of CSeq. Since it is unknown in advance when a certain potential is actually used in a mitigation effort, we averaged the carbon sequestration over a predefined period of time expressed as CSeq_sup. As such, the CSeq_sup over the time interval [t_s, t_t] is an approximation of the average net carbon sequestration over the time interval [t₀,t_e].

In the case of the establishment of a C plantation on slash and burnt natural ecosystems (Figure 5), large quantities of carbon are emitted instantaneously (i.e. E will be large). Afterwards, CSeq(t) in year t equals NEP_CP(t), assuming no CO₂ fertilization and other climate feedbacks (as such, the NEP of the natural vegetation is about 0). However, the year that a plantation starts to actually sequester carbon is postponed because the initial emissions have to be compensated (about 23 years for the example in Figure 5).

The social potential of the afforestation activities is estimated in two stages. Firstly, we establish plantations around the world using certain restrictions based on social acceptance. This is accomplished by using a particular definition of social importance: Considering only those areas that are neither needed for food and wood supply nor are covered by natural ecosystems (because of their importance for nature conservation). Establishing plantations on abandoned agricultural land is the only possibility. This leads to uptake potentials per grid cell (geographical explicit). Secondly, supply curves have been constructed for each IMAGE-2 region, summing-up the gridded sequestration potentials for all grid cells within that region where the average carbon sequestration, corrected for climate change and CO₂ fertilization effects, is positive in a year 'z' (Figure 5, 19). Since it is unknown when a certain potential is actually used in a mitigation effort, and to allow for comparison with other greenhouse gas mitigation options, the carbon sequestration is averaged over a predefined period of time (CSeq_sup(t)). Thus each point in a supply curve represents the regional sum of the average annual carbon sequestration potential of a grid cell assigned to a time interval [t_s, t_t], starting with the most productive grid cells (i.e. cells with highest sequestration rate per hectare), ending with ineffective grid cells.

The social C sequestration potential is used to determine the economic potential by linking it to costs (see 19 for details). This results in Marginal Abatement Curves (MACs) or cost-supply curves dependent on geographical-explicit environmental circumstances and possible future changes in land use. In general, the most important cost factor in producing or conserving carbon sinks is land 55. In addition, we also consider establishment costs. Other types of costs are excluded because they are either low (e.g. maintenance costs), compensated by revenues from timber, or difficult to quantify 56. Land costs are based on GTAP data 57 for land values of agricultural land around the world. Establishment costs, set at 435 US$ (1995) per ha, are uniform in time and space. This assumption is supported by the survey of Sathaye et al. 15. The value of 435 US$ (1995) per ha is based on analyzing variations between the regions and the ranges within the regions.