Biogeosciences The carbon balance of South America : a review of the status , decadal trends and main determinants

We summarise the contemporary carbon budget of South America and relate it to its dominant controls: population and economic growth, changes in land use practices and a changing atmospheric environment and climate. Component flux estimate methods we consider sufficiently reliable for this purpose encompass fossil fuel emission inventories, biometric analysis of old-growth rainforests, estimation of carbon release associated with deforestation based on remote sensing and inventories, and agricultural export data. Alternative methods for the estimation of the continentalscale net land to atmosphere CO 2 flux, such as atmospheric transport inverse modelling and terrestrial biosphere model Published by Copernicus Publications on behalf of the European Geosciences Union. 5408 M. Gloor et al.: The carbon balance of South America predictions, are, we find, hampered by the data paucity, and improved parameterisation and validation exercises are required before reliable estimates can be obtained. From our analysis of available data, we suggest that South America was a net source to the atmosphere during the 1980s ( ∼ .3– 0.4 Pg C a−1) and close to neutral ( ∼ 0.1 Pg C a−1) in the 1990s. During the latter period, carbon uptake in old-growth forests nearly compensated for the carbon release associated with fossil fuel burning and deforestation. Annual mean precipitation over tropical South America as inferred from Amazon River discharge shows a long-term upward trend. Although, over the last decade dry seasons have tended to be drier, with the years 2005 and 2010 in particular experiencing strong droughts. On the other hand, precipitation during the wet seasons also shows an increasing trend. Air temperatures have also increased slightly. Also with increases in atmospheric CO 2 concentrations, it is currently unclear what effect these climate changes are having on the forest carbon balance of the region. Current indications are that the forests of the Amazon Basin have acted as a substantial long-term carbon sink, but with the most recent measurements suggesting that this sink may be weakening. Economic development of the tropical regions of the continent is advancing steadily, with exports of agricultural products being an important driver and witnessing a strong upturn over the last decade.

predictions, are, we find, hampered by the data paucity, and improved parameterisation and validation exercises are required before reliable estimates can be obtained. From our analysis of available data, we suggest that South America was a net source to the atmosphere during the 1980s (∼ 0.3-0.4 Pg C a −1 ) and close to neutral (∼ 0.1 Pg C a −1 ) in the 1990s. During the latter period, carbon uptake in old-growth forests nearly compensated for the carbon release associated with fossil fuel burning and deforestation.
Annual mean precipitation over tropical South America as inferred from Amazon River discharge shows a long-term upward trend. Although, over the last decade dry seasons have tended to be drier, with the years 2005 and 2010 in particular experiencing strong droughts. On the other hand, precipitation during the wet seasons also shows an increasing trend. Air temperatures have also increased slightly. Also with increases in atmospheric CO 2 concentrations, it is currently unclear what effect these climate changes are having on the forest carbon balance of the region. Current indications are that the forests of the Amazon Basin have acted as a substantial long-term carbon sink, but with the most recent measurements suggesting that this sink may be weakening. Economic development of the tropical regions of the continent is advancing steadily, with exports of agricultural products being an important driver and witnessing a strong upturn over the last decade.

Introduction
This review of the carbon balance of South America, with an emphasis on trends over the last few decades and their determinants, forms part of a catalogue of similar regional syntheses covering the globe as part of the RECCAP (REgional Carbon Cycle Assessment and Processes) effort. The scope of our analyses thus encompasses all methodologies as prescribed by RECCAP, including a "bottom-up" estimation of the net carbon balance through the assimilation of component flux measurements, simulations with Dynamic Global Vegetation Models (DGVMs) and atmospheric transport inversions.
South America as a region has attracted the attention of global carbon cycle and climate researchers mainly because of the very large amount of organic carbon stored in the forests of the Amazon Basin. Occupying just less than half the area of the continent, these forests have been estimated to contain around 95-120 Pg C in living biomass and an additional 160 Pg C in soils (Gibbs et al., 2007;Malhi et al., 2006;Saatchi et al., 2011;Baccini et al., 2012;Jobaggy and Jackson, 2000; Table 1). Placing this in context, this ecosystem carbon stock (plants + soil) amounts to approximately half of the amount of carbon contained in the global atmosphere before the onset of the industrialisation in the 18th century. Thus, even if only a small fraction of this carbon pool were to be released to the atmosphere over coming decades and/or centuries as a consequence of land use change or biome shifts associated with a hotter/drier climate, then the implications for the global carbon budget (and climate change itself) would be significant. On the other hand, because of their vast area, high rates of productivity and reasonably long carbon residence times, these forests also have the potential to help moderate the global carbon problem through a growth stimulation in response to continually increasing [CO 2 ], thereby mitigating the effects of some fossil fuel burning emissions (Lloyd and Farquhar, 1996;Phillips et al., 1998). Nevertheless, this effect must eventually saturate (Lloyd and Farquhar, 2008), and hence two main factors will likely dictate future changes in forest biomass. First and of primary importance is the way in which the current fast demographic and economic development (e.g. Soares-Filho et al., 2006) will impact on all ecosystems of the region. Second, changes in ecosystem carbon densities in response to changes in atmospheric gas composition and climate (e.g. Phillips et al., 2009), perhaps also in conjunction with biome boundary shifts (e.g. Marimon et al., 2006), may also be of considerable consequence.
The continuing development of the Amazon Basin is associated directly with forest destruction mainly for agricultural use (e.g. DeFries et al., 2010). Changes brought about by altered climate and atmospheric composition on forests are subtler. Specifically, increases in carbon dioxide concentration and/or changes in direct light may stimulate tree growth and in turn rainforest biomass gains Farquhar, 1996, 2008;Mercado et al., 2009), and there is strong evidence for such a process having occurred over the last few decades and to be still on-going (Phillips et al., 1998Lewis et al., 2009). By contrast, a changing climate has, on the whole, been argued to be likely to have adverse effects on the tropical forests of the region. As for other parts of the globe, warming of the Earth's surface is predicted to result in an increase in climate variation in South America (Held and Soden, 2006), and this includes a likely increased frequency and intensity of unusually dry periods. Such increased variation, together with a general global warming, has the possibility to lead to forest decline through enhanced water stress. Drought induced forest loss may also be further amplified by fire (White et al., 1999;Cox et al., 2000;Poulter et al., 2010;Nepstad et al., 1999;Aragão and Shimabukuro, 2010). Altogether, it is the interplay between the very large area covered by high carbon density and relatively undisturbed forests with the very fast economic and demographic development, and these interacting with a changing climate, which makes South America of particular interest for its role in the contemporary carbon cycle and, in turn, to the climate of the planet over the decades to come.
This study aims to provide a state of the art assessment of the current day net carbon balance of South America through a review of carbon stocks and fluxes, their time trends, and their dominant controls. In doing this, we also describe how  Malhi et al. (2006) Tropical forest ∼ 95 Gibbs et al. (2007), Table 3 Extratropical forests ∼ 15 b Gibbs et al. (2007),  (Jobaggy and Jackson, 2000, their Table 3). e Assuming a soil carbon content of 17.7 kg m −2 (value for crops of Jobaggy and Jackson, 2000). f Both above-and belowground.
the carbon balance of South America has changed over recent decades and also provide an indication of what to expect in decades to come. In order to quantify the continent's net carbon balance, we have adopted an "atmospheric" perspective. This can most easily be envisioned as a consideration of all fluxes across an imaginary vertical wall all around the continent's margin. Any carbon leaving the box enclosed by these walls (which is also imagined to have an infinite height) is a net carbon loss for South America (and a carbon source for the atmosphere), and vice versa. From this perspective, any internal transfers within the box -for example, the flow of detritus to rivers and/or its subsequent release as respired CO 2 -is "carbon neutral" and thus does not need accounting. Similarly, although savanna fires may release substantial amounts of carbon to the atmosphere each year (van der Werf et al., 2010), only a fraction of the continental savanna area burns in each year, and the unburnt areas (almost all of which will be recovering from previous years' fires) accumulating biomass (Santos et al., 2004). Thus, as long as the total area of savanna (of any other vegetation type) remains unchanged, such "internal" fluxes can be ignored using our approach.
The paper is structured as follows. We start with a characterisation of main biomes, stocks, mean climate, climate trends, demography and economic development. We then present and discuss carbon fluxes associated with the different processes and estimate them using complementary methods. The dominant processes, considered in a loose sense, fall into the categories of fossil fuel emissions, deforestation, agriculture and trade, and forest biomass change. We then also discuss inferences from atmospheric greenhouse gas concentration data regarding the magnitude of carbon sources and sinks through atmospheric transport inverse modelling and dynamic vegetation model estimates.
2 Main determinants of large-scale land surface changes and future energy consumption

Geography, population density, demography
Of the South American nations, Brazil is geographically by far the largest, occupying ∼ 49 % of the total area of 17.8 × 10 6 km 2 , followed by Argentina (16 %), Peru (7 %), Colombia (6 %) and Bolivia (6 %). Brazil is also the dominant economy of the continent, accounting for ∼ 50 % of the continent's gross domestic product in 2009 and being the seventh largest in the world in terms of purchasing power parity (IMF, 2009). The primary geographical pattern of the continent's population distribution (Fig. 1a) involves a band of very high density along the coastal arc stretching east and south from Venezuela, the Caribbean Sea and along the Pacific down to the South of Peru, and including the mega-cities Rio de Janeiro, São Paulo and Buenos Aires. This high population density along the coasts contrasts with the very low population density in the interior, especially within the still largely undeveloped Amazon Basin which covers an area of ∼ 8 million km 2 or nearly half the continent.
South America has witnessed very fast population growth, as well as increased urbanisation over the last 70 or so years ( Fig. 2; Table 3). Rates of population growth remain substantial, but the continent-wide population is expected to stabilise at ca. 500 million inhabitants by around 2050 (Population Division of the Department of Economic and Social Affairs, UN, 2008).
In terms of "natural" ecosystem fluxes, one key region is the Amazon Basin, much of which remains covered by relatively undisturbed forest. Over half of the area of the Basin and its forest is located within Brazil (62 %), with the remaining 38 % spread across nine countries of which the largest landholders are Peru (7 %), Bolivia (6 %), Colombia (6 %), and Venezuela (6 %). As well as hosting the largest contiguous tropical forest area in the world, the Amazon Basin also abounds with a massive but still relatively unexploited mineral and other natural resource wealth (e.g. Killeen, 2007a;Finer and Orta-Martinez, 2010). To date, however, development of the Basin has been mostly limited to a clearing of natural areas (of both forest and savanna) for cultivation and pasture. Improved access to global markets has played an important role in this development, especially over recent years (e.g. Nepstad et al., 2006a;DeFries, 2010, Butler andLaurance, 2008;Finer and Orta-Martinez, 2010).

Biomes and their transformation over the last decades
Based on the remote sensing estimates of Eva et al. (2004)  forest area , with coastal temperate forests to the east. Regions further south are used for agriculture, including sugar cane plantations in Sao Paulo state for the purpose of ethanol production and still further south for cattle grazing (southeastern Brazil and Argentina). Much of the latter area was originally "Atlantic forest", having been cleared many decades ago and with less than 1 % of the original forest vegetation remaining (Dafonseca, 1985). From a carbon cycle perspective, it is of interest that, unlike the temperate and boreal regions, tropical ecosystems have not been "reset" by glaciations (Birks and Birks, 2004), and thus their soils have developed on the same substrate over very long periods (Quesada et al., 2011). As a consequence, for large parts of the Amazon soil plant-available phosphorus pools are low (Quesada et al., 2010), and phosphorus is a limiting element for growth for most forests of the Amazon Basin (Quesada et al., 2012).
Although a large fraction of the Amazon is still covered by intact forest (∼ 82 % of the Brazilian legal Amazon by 2010, e.g. Fearnside, 2005;PRODES, 2010;Regalado, 2010), land use statistics for the Cerrado region within the Brazilian legal Amazon land shows that in 2006 approximately 60 % has been used for pasture and 15 % for cultivation, with the remainder constituting degraded or managed vegetation formation types ( Fig. 3; AGROPECUARIA, Brazilian government statistics). The fraction of cultivated land has approximately doubled from 1975 to 2006, and so has its area (Fig. 3). This area change and timing matches approximately the time course and area of deforestation. Taking the area of Brazilian Cerrado (both within and outside the legal Amazon), this originally covered ca. 2 × 10 12 km 2 , but had decreased to ca. 43 % of its original area by 2004 and will be entirely converted to agricultural use by around the year 2030 if annual conversion rates stay at their current level of 0.2 to 0.3 × 10 12 km 2 a −1 (Machado et al., 2004).
The forests of the Amazon Basin have also been reduced in size at a fast pace, ∼ 0.46 % a −1 since the early 1970s (e.g.     Fearnside, 2005), with one area of forest transformation currently occurring along the so-called "Arc of Deforestation" along the steadily northwards retreating southern periphery of the Amazon forest region. According to Fearnside (2005), by 2003 16.2 % of the originally forested portion of Brazil's ∼ 5 × 10 6 km 2 of legal Amazon region had been deforested. Thus, compared to the Cerrado, a much larger percentage (83.8 %) of the forest area remains intact. This is in part due to the forest areas being more remote from economic centres, but also the soils of the forest-savanna transition zone are often more fertile than those towards the centre of the Basin (Quesada et al., 2011) and, with rainfall still sufficient, sustain a high level of crop or pasture production. The moister Cerrado regions also have the benefit of an aerial environment less conducive to crop disease pressures (Pivonia et al., 2004), especially in terms of temperature and moisture regimes that are markedly more seasonal than those of the core Amazon forest region. In addition, measures to protect Brazilian Cerrado have been far less reaching than measures to protect Brazilian rainforest (e.g. Fearnside, 2005). Quantitative data on rates of deforestation for other countries sharing the tropical forests, Peru, Colombia, Bolivia, Guyana, French Guiana, Suriname and Venezuela, are not so readily available. Nevertheless, remote sensing data covering the period from 1984 to 1994 indicate a similar relative deforestation rate for Bolivia as for the Brazilian Amazon (Steininger et al., 2001; ∼ 0.4 % a −1 ). Deforestation rates for Peru have been lower, with rates between 0.1-0.28 % a −1 gov.br/home/estatistica/economia/agropecuaria). (Perz et al., 2005;Oliveira et al., 2007) and with a deforestation rate of 0.1 % a −1 applying to recent years (Oliveira et al., 2007). Although we have not found reliable data on deforestation for all South American countries with tropical forests, a pan tropical study for 1990-1997 based on a combination of 1 km 2 and higher resolution remote sensing products (Achard et al., 2002) indicates similarly declining rates of land use change across the entire Basin as is now well documented for Brazil. For both Brazil and Peru, the declining deforestation rates over the last few years (Regalado, 2010;Oliveira et al., 2007) have risen, at least in part, as a result of new government initiatives to try and help protect these forests (see also Nepstad et al., 2006b). For the more densely populated sub-tropical and temperate zones to the south, land use change has since WWII been at even greater rates than for the tropics, specifically in Paraguay, Argentina and Chile. For these regions, many forest and woodland/scrub areas are now nearly entirely converted to agricultural use (Gasparri et al., 2008;Huang et al., 2009;Echeverria et al., 2006). The arboreal areas of the south have, however, always been of a relatively small magnitude compared to that of tropical South America (Table 4).

Climate and climate trends
Stretching from approximately 10 • N to 55 • S, South America's weather and climate can be partitioned broadly into three zones characterised by different underlying atmospheric controls. The tropical zone (extending from north of the equator to ca. 22.5 • S) has its climate determined mostly by the westerly direction of the atmospheric circulation, the monsoonal circulation during austral summer, and the influence of the Andes on lower tropospheric flow. The subtropical region's climate (ca. 22.5 • to 35 • S) is controlled by semi- permanent high pressure cells (centred around 30 • S), and finally for the mid-latitude southern part, by cyclones and anticyclones associated with the polar front in a generally westerly air flow (e.g. Fonseca de Albuquerque et al., 2009). Temperature trends over the last few decades estimated, for example, from the CRU climatology (Mitchell and Jones, 2005) reveal a warming trend for the Amazon Basin and Brazil, and constant temperatures or even a slight cooling of the continent to the south of Brazil and in the northwest of the continent (Colombia). Regarding precipitation, sufficiently long records for the purpose of robust trend analysis exist, but unfortunately, with few exceptions, these are only available for outside the Amazon Basin (e.g. Haylock et al., 2006). The pattern revealed by these data is, however, a positive trend in the region from approximately 20 • S down to Argentina and stretching from the eastern foothills of the Andes to the Atlantic coast. The second pattern is a decreasing trend in a stretch along the Pacific coast and up along the western flank of the Andes (CRU climatology; Mitchell and Jones, 2005;Haylock et al., 2006). The already mentioned increasing precipitation trend from approximately 20 • S southwards is mirrored by a strongly increasing trend of the La Plata River discharge into the Atlantic at Buenos Aires (e.g. Milly et al., 2005 and references therein). These positive trends are very likely the result of an increasing water vapour outflow from the Amazon Basin towards the south (Rao et al., 1996).
Because from a global carbon cycle perspective the Amazon Basin is by far the most significant South American region, we further describe its climate in slightly greater detail as follows. The Basin's climate is characterised by high annual mean precipitation (between ca. 1.5 and 3.5 m a −1 ) and relatively constant daily mean temperatures of 24 • to Table 4. Estimates of forested area before the onset of intense deforestation in the 20th century.

Country
Originally forested Year AD Region area a Source area (10 6 km 2 ) (10 6 km 2 )  Perz et al. (2005). 26 • C (e.g. Nobre et al., 2009;Marengo and Nobre, 2009). The main element of the seasonal variation of the climate is the austral summer monsoon, which occurs during a period from roughly early October to the end of March. The relatively small Northern Hemisphere area has a seasonal cycle out of phase with the rest of the Basin by approximately 6 months. Associated with the (austral) summer monsoon is the rainy season followed by the dry season from approximately April/May onwards. The dry season is not dry in the sense of the Northern Hemisphere mid-to-high latitudes but rather "less wet", typically defined to include months with less than 100 mm of rainfall.
The main mode of inter-annual variation over recent decades has been associated with the El Niño and La Niña oscillation, collectively referred to as the El Niño-Southern Oscillation (ENSO). El Niño phases are associated with drier conditions in the north of the Basin and vice versa (Costa and Foley, 1999). Not all variation is controlled by ENSO (i.e. Pacific sea surface temperature (SST) variations). For example, cross-equatorial Atlantic sea surface temperature differences influence the ITCZ (Intertropical Convergence Zone) location and thereby precipitation patterns as well (e.g. Yoon and Zeng, 2010). Also, on multi-decadal scales the dominance of Pacific and Atlantic influence vary (e.g. Yoon and Zeng, 2010;Espinoza et al., 2011).
Historically, Amazonian droughts have occurred fairly regularly, with a particularly intense episode in 1926 (Williams et al., 2005). Other unusually dry periods in the 20th century, mostly associated with El Niño, occurred in 1935-1936, 1966-1967, 1979-1980, 1983and 1992). In more recent years, there have been strong droughts in parts of the Amazon in 1997/98, 2005 and 2010, with the latter two apparently related to Atlantic SST anomalies (Yoon and Zeng, 2010).
Similar to global land temperature trends, the Amazon region has warmed by approximately 0.5-0.6 • C over the last few decades (1960 to 2000, e.g. Victoria et al., 1998;Malhi and Wright, 2004). Published analyses of precipitation trends by various authors differ in the periods chosen, and climatologies or station data used (Espinoza et al., 2009). This is partially due to the sparsity of precipitation records in the Amazon already noted. Nevertheless, river discharge data should also provide a good diagnostic of hydrological cycle changes with the rate of discharge to the ocean providing a measure of the Basin-wide precipitation in excess of plant requirements, and the following patterns emerge when analysing trends in Amazon river discharge at Obidos (Callède et al., 2004;Fig. 4), located approximately 800 km inland from the estuary of the Amazon River. At this point the River drains a basin of ∼ 4.7 × 10 6 km 2 , or roughly 77 % of the Amazon Basin proper. Although such data suffer from a shortcoming that the measured discharge is "blind" to whether water falling as precipitation has been recirculated via transpiration or not, as is shown in Fig. 4, the last ∼ 100 yr exhibit a substantial increasing trend (approximately 20 % change from 1900 to 2010), arguing for a similar trend in annual mean net precipitation. A second noteworthy feature which can be inferred from Fig. 4 is that wet seasons have become more pronounced and inter-annual variation has increased over the last decades.

Potential vegetation responses and feedbacks with climate
One widely cited hypothesis states that the anticipated increase in frequency and intensity of anomalously dry periods in a warming climate may lead to a large reduction in forest vegetation and replacement by savanna, grasslands or even desert by 2100 (White et al., 1999;Cox et al., 2000;19001920194019601980 Callède et al. (2004), based on data from the same datasource. Oyama and Nobre, 2003). This hypothesis has, amongst others, been suggested by the first fully coupled climate-carbon cycle modelling results (Cox et al., 2000). However, more recent versions with a further evolved coupled climate-carbon cycle model from the same institution (Hadley Centre UK) do not show such a biome switch for the Amazon region (C. Jones, personal communication). Indeed, a data-oriented analysis by Malhi et al. (2009) which corrects for the fact that climate models are predicting a too dry contemporary climate finds a much lesser effect of a changing climate on tropical forest vegetation, and a climate ensembles approach shows the likelihood of forest "dieback" to be low (Poulter et al., 2010). Thus, although the possible risk of large-scale climate change induced forest "die-back" remains a concern and requires ongoing analysis and research, when correctly calibrated only a minority of climate models predict this possibility at the current time.
Inventory data is especially of use for analysis of year-onyear features, and in some instances can give indications of what the Amazon forest response might be in a future climate state (for instance, warm years might show features that become prominent in a continually warmer greenhouse gas-enriched world). The effect of atypical dry conditions on forest function have been examined by Phillips et al. (2009) based on tree growth and mortality data of a pan-tropical forest census network. Looking at forest dynamics following the "2005 drought" they found a small but significant increase in mortality compared to the long-term pre-2005 mean rate, suggesting a potential sensitivity of forest dynamics to more frequent or intense dry periods.
Besides climate alone, the 40 % increase in atmospheric CO 2 today over its pre-industrial concentration could in principle affect functioning of vegetation, specifically increasing photosynthetic rates, decreasing stomatal density and conductance, and thus leading to higher water use efficiency (e.g. Woodward, 1987;Farquhar, 1996, 2008). There are indications based on trends in the 13 C : 12 C ratio of wood and leaf cellulose (the carbon isotopic ratio of wood is a strong function of stomatal conductance (e.g. O'Leary, 1988)) that there has indeed been down-regulation of stomatal conductance in parts of the Amazon forests (Hietz et al., 2005), although unambiguous attribution to mechanisms remains difficult (Seibt et al., 2008). Amazon River discharge and Basin-wide precipitation seem indeed, not having increased at the same rate, consistent with a trend in down-regulation of stomatal conductance (i.e. reduced evapotranspiration; Gedney et al., 2006). Higher atmospheric [CO 2 ] may also favour the C 3 photosynthetic pathway (mainly trees) over the C 4 pathway (grasses, e.g. Ehleringer and Cerling, 2002). Several studies document forest moving into savanna at the southern border of the Amazon forest-to-savanna transition zone with a speed on the order of 50 m a −1 over the last 3000 yr, this being attributed to a shift in the ITCZ (Mayle et al., 2000). Significantly higher rates of "desavannisation" over the last decades are consistent with a [CO 2 ] induced shift from C 4 towards C 3 plants (e.g. Pessenda et al., 1998;Marimon et al., 2006).

Fossil fuel and ethanol production and use
Currently, total fossil fuel emissions from South America are estimated to be 0.26 Pg C a −1 , or approximately 3 % of the global total fossil fuel emissions (Boden et al., 2011;data available up to 2007). The increase since the 1950s has been approximately exponential, with an annual increase rate of about ∼ 8 % a −1 from 1950-1980 but falling back to 3 % a −1 during the period from 1980 and S1). Use of fossil fuels on a per person (pp)  average of 1.22 Mg C pp −1 a −1 and is less than 15 % of more highly industrialised countries such as the USA (ca. 4.9 Mg C pp −1 a −1 ).
One interesting aspect of fuel use in Brazil is that around 40 % of the total fuel used for motor vehicles and other combustion engines is ethanol (C 2 H 6 O) produced through the distillation of fermenting sugar cane (Macedo et al., 2008). Nevertheless, we do also note that biofuel usage is not included in the fossil fuel totals above. Compared to other crops, the ratio of renewable energy of ethanol/fossil fuel energy used to produce ethanol is high (8.3;Macedo et al., 2008). Ethanol utilization in Brazil in 2006 was 14.1 × 10 6 m 3 . To put this into perspective, the C flux to the atmosphere from burning ethanol in 2006 amounts to ∼ 5.8 Tg C a −1 (the density of ethanol which has a carbon content of 52 % is 0.789 Mg m −3 ), which is ∼ 5 % of the total fossil fuel emissions from Brazil. However, because the carbon biomass used in ethanol production must have originated from atmospheric CO 2 as recently assimilated by local sugar cane crops, these emissions do not contribute to the net carbon balance.
Ethanol production from sugar cane in Brazil goes back to the 1920s, originally developed as a means to utilize sugar cane overproduction. Currently, the main region where sugar cane is planted is in the southeast of Brazil (

Deforestation
Historically, global deforestation carbon emissions have been based on a book-keeping approach as detailed by the pioneering study of Houghton et al. (1983). The area change data associated with land-use-change-related carbon fluxes used in these studies have traditionally been from the Food and Agriculture Organization of the United Nations (FAO), with the data provided to FAO by countries' governments (see, e.g. Houghton, 2003). More recently, independent land use change area estimates -particularly those caused by deforestation -based on remote sensing data and various statistical scaling approaches have become available (PRODES, Brazilian government; see Morton et al., 2005;Hansen et al., 2008;Achard et al., 2002Achard et al., , 2004. One advantage of these latter estimates is that they are more easily verifiable than the FAO data. Based on rates of change, it is then possible to estimate land-use-change-related fluxes based on spatially explicit forest biomass estimates, e.g. from the RAIN-FOR forest census network (e.g. Malhi et al., 2002;Phillips et al., 2009), fraction of biomass combusted, and estimates of lagged carbon release and uptake due to decomposition of dead organic carbon and recovery after deforestation, respectively (Houghton et al., 1983).
To progress along similar lines, in this study, we first compare the time course of forest area change (Fig. 7) based on FAO data (see e.g. Houghton, 2003), provided for this study by R. A. Houghton, with those coming from independent remote sensing-based estimates using sensors of various spatial resolutions. In some cases the remote sensing estimates are based on a hierarchical approach using increasingly spatially resolving sensors to first identify "deforestation hotspots" and then zoom in to hotspot areas using higher accuracy (Achard et al., 2002;Hansen et al., 2008). Figure 7 also includes estimates of changes in agricultural land use provided by the Brazilian government (Instituto Brasileiras de Geografia e Estatistica, Agropecuaria, 2006), which permits some test of consistency of the deforestation numbers. Although by no means a new insight, it is, however, clear that compared to the various independent remote sensing-based estimates (the numerical data are given in Table 5), the FAO area deforested numbers are substantially larger, even when considering that the different estimates are not for exactly the same regions. The independent remote sensing-based estimates are quite consistent amongst each other and also consistent with the estimates of changes in agricultural land use in Brazil provided by the Brazilian government mentioned earlier on. We therefore base our further attempt to estimate carbon fluxes associated with forest clearing on the published remote sensing estimates of forest area change rates (i.e. independently from the deforestation numbers of FAO).
The deforested area provides an upper bound on carbon release to the atmosphere if it is assumed that all forest carbon (including roots and necromass) and soil carbon fraction is lost after deforestation. Then the total carbon to be lost, F ld→at , is the product of the mean tree and soil organic matter carbon per area multiplied by the deforested area, A, i.e. F ld→at = r C:biom (B trees + r soil release C soil ) A. (1) Here, r C:biom is the carbon to biomass weight ratio, B trees is tree biomass per area, r soil release is the fraction of soil organic carbon released to the atmosphere, and C soil is soil organic carbon content per area. By taking into account the time lags between the decomposition of dead organic material after deforestation and similarly gradual replacement of the deforested area by a new (or potentially similar) vegetation type (Houghton et al., 1983), one can then estimate fluxes from differences in stocks. This provides a simple alternative to the accounting of individual fluxes within the continent which would involve, for example, a separation of deforestationrelated emissions caused by fire from those which form part of a natural cycle (see Sect. 1). Below, we implement a simplified version of this so-called "book-keeping" procedure with simple conceptualisation of the time lags in decomposition and time-course of establishment of a new vegetation cover. Our purpose is, in this relatively simple way, to bracket likely values of deforestation fluxes; our estimates reflecting the uncertainties of lags in carbon release and recovery whilst also taking full advantage of published deforested area estimates based on remote sensing. Specifically, we assume exponential decay of dead organic material left over from a deforestation event, i.e.
where C is the carbon stock, C the annual release of carbon to the atmosphere due to decomposing leftover debris, t a discrete time interval (one year), and λ resp a decay constant. Establishment of new vegetation is assumed to approach steady-state carbon content following where λ rgrwth is the inverse of the time scale to reach a new steady state. The total flux to the atmosphere in year t caused by deforestation during year t and decomposition of dead organic material remaining from deforestation events in previous years is where F ld→at (t, t def ) is the flux from land ("ld") to the atmosphere ("at") in year t due to deforestation in year t def in the past. Similarly, the total flux from the atmosphere to land due to re-establishment of either forest or another vegetation type (we distinguish cultivation, secondary forest and pasture) is given by where F at→ld (t, t def ) is carbon uptake in the wake of deforestation in year t def , and α lu is the fraction of originally deforested land being replaced by land use type "lu" each year (for details see Appendix). For α lu we use the values from Brazilian government statistics (AGROPECUARIA; Fig. 3), which due to lack of the same statistics for other countries we assume to be similar. The model parameters are defined and values given in Table 6. Explicit expressions for F at→ld (t, t def ) and F at→ld (t, t def ) can be derived and are given in the Appendix. Following our goal to use deforestation area estimates based on published, reproducible studies as much as possible, we have attempted an exhaustive search of the literature (Tables 5 and 7). Unfortunately, there are countries for which we did not succeed with our search. For three countries, Brazil, Argentina and Paraguay, we may reconstruct reasonably well the land use change history from 1970 onwards. To proceed, we conceptually separate tropical from extratropical forest regions. To estimate tropical area  [1990][1991][1992][1993][1994][1995][1996][1997][1998][1999]. For extratropical South America we use the sum of the Argentina and Paraguay numbers. This will lead to a small underestimate because we neglect Chilean and Uruguayan deforestation. For all of South America, α lu is derived from Brazilian government statistics (AGROPECUARIA; Fig. 3), thus assuming the same land use time history after deforestation for all of South America.
Simplifications and sources of uncertainty include the limitations due to the simple model formulation itself, the use of a spatial average wood density (supported by an analysis of RAINFOR data), scaling of deforestation area estimates, assumption of similar land use transition time patterns in South America as in the legal Amazon region, and uncertainty in the time scales for the decay of forest debris after deforestation and for the re-establishment of a new vegetation type after deforestation. Error propagation yields a total uncertainty  Killeen et al. (2007b), based on remote sensing (Landsat images, wall-to-wall). g Oliveira et al. (2005), based on remote sensing (Landsat images, wall-to-wall). h Perz et al. (2005). i Huang et al. (2007), based on remote sensing. j Assuming that Atlantic forest region is where most forest is being cleared. k Atlantic forest only. l Gasparri et al. (2008), based on remote sensing (Landsat images, wall-to-wall).
of the annual flux to the atmosphere due to deforestation of approximately ±25 % (see Appendix).
Our estimates indicate a net flux to the atmosphere of around 0.5 Pg C a −1 due to deforestation and land use change in South America over the last two decades or so (Figs. 7  and 8). This has persisted over the last few years, despite the remarkable decrease in deforestation in the Brazilian Amazon, because of lagged fluxes caused by earlier deforestation. Our estimate is smaller than the FAO estimate used in the recent study of Pan et al. (2011) for South America. The difference is smaller than expected based on the estimates of deforested areas alone, which by themselves differ strongly (Fig. 7). This is because the net flux to the atmosphere is the difference of release and regrowth and the regrowth estimate of Pan et al. (2011) is also much larger than ours. Thus, the differences tend to compensate each other, and thus the global budget is not changed much.

Amazon forest censuses
Forest carbon storage and its trends have been monitored over the last few decades by keeping track of the diameter of all living trees within a permanent plot network. Two measurement strategies have been followed. One strategy (the CTFS (Center for Tropical Forest Science -Smithsonian Institution) approach) samples a few plots of a relatively large size, 16-50 ha, of which there are currently three in tropical America . The other (the RAINFOR network; Phillips et al., 2009) currently samples 136 plots, mostly of 1 ha, covering the main axes of forest growth variation (El Niño, soil fertility, dry season length; O. Phillips, personal communication). The censuses from the RAINFOR network have revealed a positive trend in aboveground biomass growth in the Amazon (dry matter, in units ha −1 a −1 ) reported first by Phillips et al. (1998) and recently summarised in Phillips et al. (2009). These measurements do not include soil carbon trends, but this time series of inventory data is a significant step forward in understanding recent trajectories in the amount of carbon stored by Amazon forests. Given the labour and logistically-intensive requirements associated with working in remote locations, then inevitably the number of plots remains relatively few compared to what might be considered ideal, and, of course, that data is only available for the last few decades. Thus, there has been some concern expressed that the biomass accumulation (NEP) estimates are biased toward high estimates because rare large-scale disturbance events involving large biomass losses have not been captured . Nevertheless, an examination of this concern  has concluded that, using a realistic (observed) disturbance severity and return time distribution, the results of a positive forest biomass gain trend based on the existing census network remain statistically significant and are unlikely to be an artefact. Other criticisms such as the uncertainty induced by using allometric equations for biomass estimation have been assessed and have also been demonstrated to have only minor impact on the regional sink estimates . Results from a similar analysis based on the CTFS forest plots has confirmed a pan-tropical biomass increase trend, although of lesser magnitude . Here we do not use the results from this latter study, especially as only one plot is located in tropical South America.
We extrapolate the biomass changes reported by  to the tropical forests of all tropical South America by first assuming a carbon content of wood of 50 % by dry-mass. Furthermore, following the compilation of Lewis et al. (2009;Supplement, p. 30) for estimating intact forest area in the year 2000, we obtain a value of 703.3 ± 142 × 10 6 ha (the value used is the mean of 630.5 × 10 6 ha from GLC 2000 (Global Land Cover Mapping for the Year Fraction of dead biomass immediately released to the atmosphere after a deforestation event (Houghton et al., 1983). α lu Fraction of originally deforested land being replaced by land use type lu where lu can either be cultivation, secondary forest, or pasture. We estimate these fractions from agricultural statistics for the legal Amazon (AGROPECUARIA, Brazil) and assume the same ratios throughout South America. C oldgrowth forest = r C:Bio (1 + r blwgrd:abvgrd ) Mean alive forest tree carbon content per area based ·220 (Mg C ha −1 ) on RAINFOR forest censuses. C forest soil = 291 (Mg C ha −1 ) Oldgrowth forest soil carbon content per area (Jobaggy and Jackson, 2000).
Carbon per area in vegetation of pasture (Barbosa and Fearnside, 1996).
Carbon per area in cultivation vegetation (Barbosa and Fearnside, 1996). C secdry forest = 0.8 * C oldgrowth forest Carbon per area in secondary forest vegetation (based on RAINFOR data). r blwgrd:abgrd = 0.2 Ratio of below-to aboveground tree biomass (Malhi et al., 2010). r soil release = 0.22 Fraction of soil C released to the atmosphere when forest is converted to agriculture (Murty et al., 2002) (while according to Murty et al., 2002 the transition of forest to pasture does not lead to significant soil carbon loss). r C:Bio = 0.5 Ratio of carbon to rest of tree biomass by weight, λ oldgrowth forest = 0.05...0.1 a −1 biomass decay rate of primeval forest debris after deforestation (Achard et al., 2002). λ secndry forest = 0.05 a −1 Spin-up time scale for establishment of secondary forest after deforestation (Schroth, 2002).
r C:DW ∼= 0.5 is the ratio of carbon to dry weight of trees, A 0 is the area of intact forest in 1970 before intense deforestation started (∼ 817 × 10 6 ha), λ ≈ 0.0046 (i.e. approximately 0.46 % forest area lost per year), estimated from deforestation numbers based on PRODES from 1988 onwards and estimates of Fearnside (2005) from 1970 to 1988 (Table 5). We also assume a belowground to aboveground tree biomass ratio of r BG:AGB = 0.2 based on Malhi et al. (2009). The resulting flux estimates are listed in Table 12 and shown in Fig. 9. The main features are a long-term  carbon sink of 0.39 ± 0.26 Pg C a −1 in the mean (the uncertainty includes the contribution from area estimate variation) with a reduction in the sink from 2005 onwards due to  Table 4, (iv) same as (iii) but including in addition published remote sensing-based estimates for the rest of South America as listed in Table 4, (v) deforestation rate by area for Latin American humid tropical forests of Achard et al. (2002) based on remote sensing, (vi) same but for South America as estimated by Hansen et al. (2008), and (vii) total change in cultivated area per year due to agriculture in Brazil based on Brazilian government statistics (UNICA, http://www.unica.com.br/dadosCotacao/estatistica). Year AD Carbon flux to Atmosphere (PgC yr −1 ) Net Flux to Atmosphere for λ oldgrowth_forest =0.096 Net Flux to Atmosphere for λ oldgrowth_forest =0.048 Net Flux to Atmosphere if carbon is released immediately and no regrowth Land carbon gain due to recovery to pasture Land carbon gain due to recovery to cultivation Land carbon gain due to recovery to secondary forest Fig. 8. Estimates of carbon released to the atmosphere from South America due to deforestation for two scenarios: (i) carbon is released gradually and regrowth is taken into account using a simplified book-keeping model following Houghton (1983) as described in Sect. 3.2 and the Appendix, and (ii) all forest carbon after deforestation is released immediately to the atmosphere and there is no regrowth. the on-going decomposition of dead trees arising as a consequence of unusually high mortality rates due to drought conditions in that year ). This carbon associated with the drought-associated mortality spike (∼ 1.2 Pg C) is modelled as not to have been released to the atmosphere immediately, but rather decaying exponentially in time and thus reducing the Amazon Basin forest sink for several years to come.  Gasparri et al. (2008) 1980-1989138 Gasparri et al. (2008) 1990-1999202 Gasparri et al. (2008) 2000 208 Gasparri et al. (2008) a Assuming that the Atlantic forest region is where most forest area is being cleared.

Inferences from atmospheric CO 2 concentrations and atmospheric transport
Depending on whether the land is a source or a sink, the effect of a carbon flux between land and the atmosphere is to either increase or deplete the CO 2 concentration in the overlying air column. By keeping track of an air parcel's path over a region of interest and by measuring the air column CO 2 increase/decrease along the air parcel path, it is thus possible, in principle, to estimate integrated net fluxes along the path. More generally, spatio-temporal concentration patterns in the troposphere contain information on surface fluxes, which theoretically can be extracted by inverting and un-mixing the effect of atmospheric transport and dispersion. This is done in practice using a 3-D atmospheric transport model in an inverse mode. For tropical South America, and the tropics generally, two obstacles do, however, make such an approach currently unreliable. First and foremost, the troposphere around and inside the continent is highly under-sampled. Inverse methods can potentially provide information from remote observations in the tropical marine boundary layer or in the temperate latitudes. However, both transport modelling shortcomings and the inherent atmospheric dispersion that occurs over transport times of weeks from the tropical land surface to remote sites hamper that approach. As Stephens et al. (2007) showed for the tropics as a whole, tropical land flux estimates derived statistical uncertainties are very large, which reflect the loss of information during the transit of air-masses to the remote observation sites. The flux estimates based on classical atmospheric transport inversions in Fig. 10 reveal large scatter in the estimates among models, confirming our assessment of bias. Given that the estimates may largely reflect noise, we conclude their results not to be useful for the purposes of this study.
A new development with atmospheric sampling over South America is that recently joint efforts by IPEN (Sao Paulo, Brazil), NOAA-ESRL (Boulder, USA), University of Leeds (Leeds, UK) and University of Sao Paulo (USP) have led to regular vertical aircraft-based greenhouse gas sampling, with one/two stations (Santarém, Manaus) operating since approximately the year 2000 and four aircraft sites from the end of 2009 onwards. These data should provide the necessary information to allow an atmospheric approach to be successfully applied for the quantification of the carbon sources and sinks associated with both human activity and natural biological processes, integrated across the Amazon Basin. An air parcel back-trajectory-based columnintegration technique applied to the 10-yr record from Santarém reveals a moderate net carbon source of the land region upstream of Santarém, and when fire related fluxes are subtracted on the basis of CO column enhancements, an approximately balanced land surface is found (Gatti et al., 2010). The region upstream of Santarém covers only 10-20 % of the Basin and includes not only forests but also forest converted to agricultural use, as well as savanna and grasslands. It is thus quite likely that the balance of the entire Basin differs from this result.

Estimates from dynamic global vegetation models (DGVMs)
For this study modelling results from five DGVMs have been made available to us (TRENDY project, Sitch, personal communication). The models (DGVMs) were applied globally with common climate forcing and atmospheric [CO 2 ] over the historical period 1901-2009 from a combination of ice core and NOAA annual resolution   Table 8 and the flux estimates in Table 11. The main features of the simulation results of net biome productivity (NBP) (Fig. 11), where NBP is defined as where N B is net biome productivity of land vegetation, R H heterotrophic respiration of land vegetation, F losses due to fire and Q R carbon lost by riverine export, are as follows.
Inter-annual and decadal variability of the model predictions are similar, nonetheless differences become apparent when fluxes are cumulated over time. With regards to cumulated changes in pool sizes, simulation results can be grouped into three sets. One model (LPJ) predicts a balanced land vegetation; three models a moderately carbon-gaining vegetation (SDGVM, TRIFFID and OCN); and the last model substantial carbon gains (HYLAND). With the exception of LPJ, all model predictions suggest a regime shift around 1970 towards an increase in carbon gains. Overall, on longer time scales there is substantial divergence in the predictions, indicating that processes relevant to longer term changes may not be properly captured and/or represented by the models at this stage of their development. Thus, we have not included them in the current synthesis.

Agricultural and wood production and exports
For our estimates of carbon fluxes related to deforestation, we have assumed implicitly that all carbon related to agricultural use of originally forested land remains in the country. However, increasingly agricultural products are being exported (Fig. 5). Specifically for Brazil there is a strong trend over the last decade of soybean products and meat from cattle. In terms of carbon the amounts remain small (Tables 9  and 10), and so even with large uncertainties, at present the contribution to the overall carbon budget is negligible. It is worth noting that according to DeFries et al. (2010), trends in deforestation are strongly related to increasing exports (see also Nepstad et al., 2006a).

Role of additional components: rivers, volatile organic carbon compounds (VOCs), fire
For the carbon balance of South America as we have defined it in Sect. 1, riverine carbon discharge to the oceans constitutes a small carbon net loss (i.e. a sink) due to export of dissolved and particulate carbon both from weathering and biomass production. We consider here just the loss of carbon via this route by the Amazon River. Inorganic carbon from weathering is ∼ 0.02 Pg C a −1 (Probst and Mortatti, 1994) and of organic carbon ∼ 0.05 Pg C a −1 (Richey et al., 1990).
These numbers are small because most organic carbon transported by rivers outgasses within the Basin and thus cancels in a hydrological basin-wide carbon balance. In addition to CO 2 , other carbon containing gases, primarily CH 4 and CO, contribute to the overall carbon balance of Amazonia in minor ways. CH 4 , CO and volatile organic carbon compounds (VOCs) are all emitted from the terrestrial biosphere. With the carbon within these emitted compounds having to have sometime previously been assimilated into the terrestrial carbon pool through photosynthetic CO 2 fixation (with a lag time to their release ranging from seconds to centuries) from the perspective of a carbon balance, these fluxes cancel out. Nonetheless, for completeness we discuss briefly the nature and magnitude of these emissions of carbon in chemically reduced forms. CH 4 originates dominantly from anaerobic environments, including permanent wetlands, seasonally flooded forests (e.g. Melack et al., 2004), rumens of buffaloes and cows, and from rice paddies. It is also emitted during the dry season from biomass burning (e.g. van der Werf et al., 2010). While no direct evidence has been found in Amazonia for aerobic plant emissions (Keppler et al., 2006;do Carmo et al., 2006), emissions have been observed from forest canopies, possibly originating form arboreal termites or anaerobic microsites (Patrick Crill, personal communication). Annually averaged emissions for eastern Amazonia, based on atmospheric measurements, which implicitly integrate over all known (and unknown) sources are ∼ 30 mg CH 4 m −2 d −1 , or just 0.02 g C m −2 d −1 . In contrast, Gatti et al. (2010) reported net CO 2 emissions in the wet season of 0.44 ± 0.38 g C m −2 d −1 and 0.35 ± 0.17 g C m −2 d −1 in the dry season. Although total methane fluxes do not have a significant impact on total carbon balance, their radiative forcing contribution is significant because of its roughly 20-fold higher greenhouse gas efficiency (on a mass basis) (Lashof and Ahuja, 1990).
Annual Amazon emissions of CO appear to be dominated by emissions from biomass burning, but there is also a contribution to CO emissions (evident during the wet season; viz. Fig. 10; Gatti et al., 2010) originating from direct soil emissions (Conrad and Seiler, 1985), direct plant  emissions (Guenther et al., 2006) and via rapid oxidation of isoprene emissions to CO (Kuhn et al., 2007). Gatti et al. (2010) estimated emissions of 27 mg CO m −2 d −1 during the wet season, which translates to just 0.01 g C m −2 d −1 ; clearly a very minor part of the overall carbon balance. Annually averaged CO emissions including both fire and other processes average roughly 150 mg CO m −2 d −1 , equivalent to 0.06 mg C m −2 d −1 . Taken as a whole, CH 4 , CO and VOCs (implicit within the CO totals), appear to contribute less than 0.1 mg C m −2 d −1 (i.e. Basin-wide on the order of 2 × 10 −3 Pg C a −1 ) to the overall carbon balance, with CO from fires most important for carbon balance and CH 4 more important for radiative forcing.

Synthesis
As policymakers try to determine the best route to mitigation of carbon dioxide release as a consequence of fossil fuel burning, and climate research strives to assess the extent to which the land surface can "draw-down" atmospheric CO 2 in to the future, it is becoming increasingly important to understand all components of the global carbon cycle. In particular, detailed regional studies are needed to close the carbon balance. Here we have attempted this for the South American continent. Although our study is by no means complete, by relying on those data and estimates for which sources are clearly  1975-1979 1980-1984 1984-1989 1990-1994 1995-99 2000-2004 2005-2009 Fossil fuel burning Deforestation 0.12 ± 0.012 0.14 ± 0.014 0. traceable and for which we have only limited methodological concerns, viz. fossil fuel emissions, estimates of intact forest growth, deforestation and exports of agricultural products, we find that South America was a net source to the atmosphere during the 1980s (∼ 0.3-0.4 Pg C a −1 ) and has been close to neutral (∼ 0.1 Pg C a −1 ) in the 1990s with carbon uptake in old-growth forests nearly compensating for carbon losses due to fossil fuel burning and deforestation ( Fig. 9; Table 12). The one study employing an atmospheric approach which we have confidence in methodologically is broadly consistent with these results (Gatti et al., 2010). The situation seems to be changing over the last decade. Although annual mean precipitation over tropical South America (as diagnosed by river discharge) has generally a long-term upward trend, dry seasons have tended to become drier/longer (and thus wet seasons have been wetter). It is currently unclear what the effect of these climate changes on the old-growth forest carbon sink will be. However, first measurements seem to indicate that it may be weakened at least in drought years. Accordingly, the carbon balance of South America may have started turning towards being a weak source to the atmosphere in the 2000s. Finally, the development of the tropical forest regions of the continent is advancing steadily with exports of agricultural products being an important driver of land use change and with exports witnessing a strong upturn over the last decade.

Simplified Houghton style book-keeping model to estimate carbon release to the atmosphere after deforestation
As mentioned in the main text, we assume exponential decay of dead organic material left over after a deforestation event: C = −λC t, where C is carbon, t a discrete time interval (one year), and λ decmp a decay constant. Thus, the carbon release during t − t def years after the deforestation event in year t def is F ld→at (t − t def ) = λ decmp (1 − λ decmp ) t−t def −1 C(t def ) with C(t def ) = r C:Bio B trees A(t def ) Total dead biomass due to clear-cutting of area A (1 − α) fraction of dead biomass not immediately released +r C:Bio r soil release C soil , where r C:Bio is the carbon to mass ratio of wood, B trees is tree biomass per area (Mg ha −1 ), and C soil is forest soil organic carbon. The total flux to the atmosphere in year t caused by deforestation during previous years and subsequent decomposition of remaining dead organic material is Similarly, as already mentioned as well, the time course of carbon uptake by land due to establishment of a new vegetation type after deforestation is assumed to follow C(t − t def ) = C steady (1 − e −λ rgrwth (t−t def ) ), where λ rgrwth is the inverse of the time scale to establish the new vegetation type. Therefore F ld→at (t −t def ) = r C:bio B lu A(t def )(1− e −λ lu t )e −λ lu (t−t def ) .
The total flux from the atmosphere to land due to reestablishment of either forest or another vegetation type (we distinguish cultivation, secondary forest and pasture) is then given by F tot where F ld→at (t, t def ) is carbon uptake in year t in the wake of deforestation in year t def and is the fraction of originally deforested land being replaced by land use type lu, thus altogether The net flux to the atmosphere in year t finally is F net (t) = F tot ld→at (t) − F tot ld→at (t). A list of variables and their assigned values to estimate fluxes to and from the atmosphere as a consequence of deforestation and subsequent land use change are given in Table 6 of the main text.
As stressed in the main text, the purpose of the bookkeeping model is to obtain realistic brackets of the fluxes from and to the atmosphere associated with deforestation and land use change based on a model level of complexity matching approximately the level of detail of the available data. The model is centred around the most robust piece of information which is area deforested. Causes of uncertainty in net flux estimates based on this model are due to uncertainty in (i) deforested area -approximately ±10 %; (ii) biomass per area -the largest contributor is the uncertainty in primary forest biomass, which based on the RAINFOR plot data we estimate to be in the range of 210-230 t ha −1 ; the uncertainty induced is thus approximately ±5 %; (iii) fraction of land use after deforestation -since the largest carbon release by far is from brazil and the stocks of pasture and agriculture are small, the error is quite small, on the order of ±5 %; (iv) decay and spin-up time scales -the largest influence on the results due to uncertainty in the spin-up time scales is the decay constant of primary forest debris; the uncertainty due to this factor is assessed by doubling the constant and recalculating the fluxes shown in Fig. 8. Altogether we estimate the total uncertainty of our flux estimates to be ±25 %.