Size and frequency of natural forest disturbances and the Amazon forest carbon balance

Forest inventory studies in the Amazon indicate a large terrestrial carbon sink. However, field plots may fail to represent forest mortality processes at landscape-scales of tropical forests. Here we characterize the frequency distribution of disturbance events in natural forests from 0.01 ha to 2,651 ha size throughout Amazonia using a novel combination of forest inventory, airborne lidar and satellite remote sensing data. We find that small-scale mortality events are responsible for aboveground biomass losses of ~1.7 Pg C y−1 over the entire Amazon region. We also find that intermediate-scale disturbances account for losses of ~0.2 Pg C y−1, and that the largest-scale disturbances as a result of blow-downs only account for losses of ~0.004 Pg C y−1. Simulation of growth and mortality indicates that even when all carbon losses from intermediate and large-scale disturbances are considered, these are outweighed by the net biomass accumulation by tree growth, supporting the inference of an Amazon carbon sink.

G lobal records of atmospheric CO 2 concentrations, fossil fuel emissions and ocean carbon uptake, estimated on the basis of ocean surveys, indicate that there is a large terrestrial carbon sink 1,2 of which a substantial portion may be due to uptake by old growth tropical forests 3 . On the other hand, were some of the current large tropical forest carbon pools (including B100 Pg C in aboveground biomass (AGB) in Amazonia 4,5 ) to be released rapidly to the atmosphere 6 , it would substantially enhance greenhouse warming 1 . Understanding the nature and trajectory of the Amazon forest carbon balance is therefore of considerable importance.
The evidence for a tropical old-growth forest sink 7,8 is based primarily on repeated biometric measurements of growth and death of individual trees across the tropics. These measurements indicate that at the plot-level old-growth forests in Amazonia and Africa have apparently gained carbon over the last 30 years [8][9][10][11] . The extrapolation of regional trends from a relatively small number of B1-ha-sized plots has been questioned because potentially undersampled natural disturbances at the landscapescale could counterbalance tree level growth 12,13 . Thus, according to this view, forest plots are biased towards those parts of the landscape recovering from natural disturbance.
Resolving this issue requires assessing whether estimates of biomass gain are robust when fully considering disturbances of all sizes 14,15 ; here we test this statistically against the null hypothesis of net zero change in biomass. We synthesize and characterize the frequency distribution of natural disturbance at all spatial scales across forests of the Amazon region using a combination of forest censuses, airborne lidar and passive optical remote sensing from satellites ( Fig. 1). We ask whether the net biomass gains inferred from forest census data are an artefact of the small size and limited number of plots in the plot network 10 . We address this question using a simple stochastic forest simulator based on growth statistics from the forest census network and the new regional disturbance size-frequency distribution scaled to all Amazon forest regions. We find that large-scale blow-downs and medium-sized disturbances have a minor impact on AGB change of South American tropical forests. Moreover, taking into account the full range of natural disturbances, we find support for the inference of a carbon sink in natural Amazonian forests.

Results
Amazon-wide frequency distribution of natural forest disturbances. There are two spatially disjoint size and severity domains of large disturbances in the Amazon: one domain with large blow-downs centred west of Manaus and another large one where the largest blow-downs are absent (Fig. 2). Although it has been suggested that the disturbance size frequency distribution follows a power law p(x)px À a (probability density p(x) and size of an event x) 16 , the observed distribution suggests a more subtle picture (Fig. 3). Visually three sections may be identified: an approximately exponential decline of frequency with size for smallest size disturbances, a power law-type decline for intermediate scales and another power law decline for the largest-scale disturbance blow-downs (Fig. 3a,c). The power law decline for intermediate disturbances with size appears to be steeper than for largest blow-downs. This is seen in the estimated return intervals versus disturbance severity relationship (see Methods) that reveals a sharp increase to higher values for intermediate range disturbances from 1 to 10 ha (Fig. 3b,d). The data also show that disturbance-induced tree mortality that cause small-area disturbances have a return interval of B100 years (Fig. 3b,d). This agrees with studies from other tropical forest regions that observed an annual tree-fall disturbance rate of 1% by the process of gap formation due to tree death 17 . By contrast, the return interval of large blow-downs is very long-that is, such events are extremely rare-ranging from 4 Â 10 5 year to 410 7 year depending on size (Fig. 3b). Small disturbances (o0.1 ha) per year are many orders of magnitude more frequent (B10 10 events) than large blow-downs (B10 3 events) over the Amazon (Fig. 3a).
Forest biomass loss from disturbance. Based on the size and frequency of natural disturbances of our data (Fig. 1 18 , the total carbon released by natural disturbances is estimated as 1.88 Pg C y À 1 , where B1.66 Pg C y À 1 or B88.3% is accounted for by smallscale mortality (o0.1 ha), B12.7% from intermediate (0.1-5 ha) and B0.02% from large disturbances (Z5 ha). Large disturbances although visually impressive are extremely rare (Fig. 3b,d), and the estimated amount of biomass loss is only 0.004 Pg C y À 1 . By comparison net carbon emissions caused by forest clearing in the Brazilian Amazon 19 in the 1990s were B0.2 Pg C y À 1 . Conversion of the mortality to Amazon forest areas implies that natural mortality affects 2.0 Â 10 7 ha y À 1 or 2% of total forest area, where B80.0% is from small-scale mortality, B19.9% is from intermediate and only 0.1% from large disturbances.
Implications of natural forest disturbances for the carbon cycle. The estimated disturbance spectrum permits us to address whether the observed carbon balance of the Amazon tropical forests inferred from forest plot censuses does indeed statistically significantly reflect carbon gain (carbon accumulation rates significantly greater than zero). For this purpose we use a stochastic forest growth simulator 10 of the form dM ¼ G Â dt-D Â dt, where dM is aboveground forest biomass loss in units of carbon per area, dt a time interval, here 1 year, and G and D stochastic variables distributed according to the observed distributions of aboveground mass gain due to growth (G) and loss (D) due to mortality 10,12,20 (for details please see Methods). We use the simulator to assess the mean net carbon balance and its s.d. We simulated 10 9 equivalent annual observations of each scenario and statistical significance of the results is assessed using a t-test ( Table 1). The scenario that we consider to be most realistic for the whole Amazon region is marked bold in Table 1. For all scenarios ensemble mean net gains are positive and for all but the most extreme scenario, the t-tests reveal significance. Intermediate disturbances have a notable effect on the mean but relatively small effect on the variance. In contrast, large disturbances have no perceptible effect on the mean but greatly increase the variance. The exceptional scenario-which given our data are clearly over-pessimistic-assumes both that the largest blow-downs occur not only in Central Amazonia but throughout the Amazon forest regions, and that intermediate disturbances occur at a rate that greatly over-represents the importance of fluvial disturbances (Supplementary Table 2).

Discussion
In summary, we have characterized the full size distribution and return frequency of natural forest mortality and disturbance in the Amazon forest biome (Fig. 3). Our findings help to resolve the debate about the relative importance of intermediate-and larger-area disturbances 10,12,13,20 and gains in biomass stocks in tropical forest plots 10 for determining the regional-scale carbon balance. In our simulation taking into account the full range of natural disturbances, we find significant increases in the biomass of Amazonian forest. Although the simulation does not consider the spatial and temporal interactions of growth and disturbance, these results nonetheless imply that natural disturbance processes in Amazonia are insufficiently intense or widespread to negate the conclusion from the pan-Amazon plot network that old-growth forests in that region have gained biomass. Uncertainty about the role of disturbances in affecting estimates of the long-term trajectory of the carbon balance of tropical forests is declining as the forest-monitoring effort on the ground increases both in time and space 8-10,21 . Our characterization of the natural disturbance regime of the Amazon forest yields new insight into the role of disturbance in tropical forest ecology and carbon balance.

Methods
Assessing the range of natural forest disturbances. Our approach includes natural causes of tree mortality 14 (including partial mortality such as branch falls) that liberate carbon 6 , but excludes anthropogenic disturbance caused by forest   24 , and large area disturbances from blowdowns using two data sets 25,26 from Landsat satellite images in an East-West transect 25 and over the entire Brazilian Amazon forest 26 (Fig. 1). For small-area disturbances we estimate biomass loss associated with area loss of each event of disturbance. For intermediate disturbances several assumptions are required to translate the measurements of forest structure from B1 m airborne lidar data into an estimate of biomass loss ( Supplementary Figs 2 and 3). To ensure that our test of the hypothesis that the plot network effectively measures biomass change is as robust as possible for natural forests ( Supplementary Fig. 4), our assumptions conservatively err on the generous side to the magnitude and frequency of intermediate disturbance. For large disturbances, we reanalyzed records of blow-downs likely caused by downdrafts associated with convective clouds 27 covering Brazilian Amazon forests 26 using historical Landsat satellite images (pixels sizes B30 m) ( Supplementary Fig. 5) and a more recent East-West mosaic of Landsat scenes covering a portion of the Amazon 25 (Fig. 1d). Combining the spatial records of large disturbances detected by Landsat 25,26 with a recently developed map of AGB 5 , we estimate carbon loss associated with these large disturbances (Figs 1d and 2). Because of the uncertainties associated with belowground biomass 1,2,5,19 , we discuss carbon losses only in terms of AGB, which probably accounts for B80% of live biomass in Amazonia 4,5,19 .
For determining the largest blow-downs we build on an earlier study of large natural disturbances 26 that identified 330 blow-downs Z30 ha distributed in 72 Landsat scenes from the total 137 scenes ( Supplementary Fig. 5) acquired between 1988 and 1991 across the B3.5 Â 10 6 km 2 forested area of the Brazilian Amazon 18 . Subsequent digital image processing for blow-down detection 25 in the Central Amazon collected around the year 2000 (27 Landsat scenes) further revealed a substantial number of medium-sized blow-downs (5-30 ha) not detected using earlier visual inspection methods 26 . In both studies 25,26 spatial analysis showed a high concentration of all detected blow-down disturbances west of B58°W clearly associated with areas of strong convective activity 27 as measured from cloud-top temperatures from the TRMM satellite 25 . Reanalyzing that data 26 here using a Gaussian kernel smoothing algorithm for cluster analysis 28 confirms the concentration of blow-down disturbances in the western Amazon (Fig. 2) with blow-downs 12 times more frequent west of 58°W than to the east. This conclusion does not depend on the bandwidth size used for the cluster analysis ( Supplementary Figs 6-8).
Forest inventories and remote sensing to assess disturbance. Effective detection of forest disturbance that results in tree mortality 2,9,12,13,20,23 and the release of carbon to the atmosphere 1,2,6,19 requires observational methods that encompass relevant spatial scales 1,14 . We combine repeat measurements from forest censuses with analysis of Landsat and lidar data permitting us to estimate mortality across all relevant spatial scales (Fig. 1). For mortality that affects less than B0.1 ha, we combine two spatial and temporal sources of data: (1) 484 forest plot censuses from 135 (B1 ha) permanent plots covering 1,545 census years of tree-by-tree measurements, distributed over the entire Amazon region including the Guiana Shield (see Supplementary Methods), from the RAINFOR network that covers 45 Amazon regions 10 and (2) losses of biomass in areas of branch or tree-fall gaps 6,12,17 of two plots of 53 and 114 ha from the Tapajós National Forest in the Eastern Brazilian Amazon 23 . To estimate disturbances at an intermediate area (from 0.1-5 ha) we used a large area of airborne lidar data from four samples in the Southern Peruvian Amazon 24 covering in total 48,374 ha. For disturbances covering large areas (disturbance size Z5 ha) we combine three remote sensing data sets: (1) a spatially extensive record of large disturbances from blow-downs Z30 ha from 128 Landsat scenes from the Brazilian Amazon and 8 scenes from outside of Brazil 26 , (2) a highresolution study of blow-downs Z5 ha using 27 Landsat scenes on an east-west transect in the central Amazon 25 and (3) a multi-sensor remote-sensing product of AGB for the tropics 5 . For all mortality (Table 1; Supplementary Fig. 9 and Supplementary Table 1) we estimate areas and biomass defined as losses in AGB stocks ( Supplementary Fig. 3). For forest plot data we estimated area losses from biomass losses assuming a constant biomass density (see Supplementary Methods). We caution that this approach assumes that all biomass disturbances are linearly correlated with area of the disturbances, which is a rough approximation 14 .
Return interval versus disturbance size. To estimate return intervals of forest area loss events of a given size we first scale-estimated number frequencies to the full Amazon forest by multiplying them with the ratio AAmazon

ASample
, where A Amazon (6,769,214 km 2 ; INPE 18 , Supplementary Fig. 4) is the total forest area of the Amazon and A Sample is the sample area. The empirical probability p*(A)DA that a fixed location will be affected by a disturbance of area A during 1 year is then AAmazon Þ, where the sum is over all events across the Amazon region with area A 0 in the interval (A, A þ DA) and DA is a finite area interval. The probability P(A event ZA) for the occurrence of a disturbance event per year with area loss larger than A at a fixed location is then AAmazon (that is, not 1, therefore the notation p* instead of p), where N is the total number of observed disturbances and A disturbed total ¼ P all disturbance i¼1 A i is the total annually disturbed forest area in the Amazon. Therefore, an estimate for the return interval t(A event ZA) of a disturbance event with forest area lost larger than A event at a fixed location is given by the inverse of the probability of observing such an event per year: PðAevent!AÞ . An analogous equation holds for the return interval with respect to biomass loss associated with a disturbance event.
Forest AGB simulation. Once the disturbance spectrum of AGB loss is defined we can infer the s.d. introduced into an ensemble of growth rates from forest censuses using the simple stochastic forest simulator of the form dM ¼ G Â dt-D Â dt introduced above, which predicts forest carbon mass change per area (M) due to growth (G) and loss (D) due to mortality 10,12,20 during the time interval dt. For G we used as input parameters growth from 484 forest censuses 10 covering N ¼ 135 plots and N ¼ 1545 census years, and mortality (AGB loss) from our new disturbance spectrum analysis. To generate random numbers distributed according to our observed distribution we use the inverse transform method 10 . For growth we use specifically GBN(m,s) with m ¼ 2.5 or 2.75 (Mg C ha À 1 y À 1 ), respectively, and s ¼ 0.85 (Mg C ha À 1 y À 1 ), the mean value for the Amazon region according to the RAINFOR data 10 and Eastern Amazon, respectively. For D, we used our Amazon forest mortality frequency distribution (Fig. 3) and modifications thereof for the purpose of sensitivity and uncertainty analysis of our approach (see main text and Table 1 and Supplementary Table 2). The growth component of the simulation model is conservative with respect to the hypothesis of net biomass gains, as it neglects the growth enhancement after disturbance events 29 and so overestimates the period of biomass decline. In real forests, disturbance-recovery growth enhancements shorten the total period for which disturbance-induced net biomass losses occurs for any given patch of forest, and therefore mitigate the impact of disturbance events on the summary statistics of net biomass trajectories.
To ensure that the simulation of disturbances is operating correctly we checked the predicted Amazon disturbance spectrum against the observed spectrum using a sample of 5 Â 10 8 simulation runs, also revealing that such a number is sufficient to reproduce the full spectrum. The simulator was then run for 10 9 annual equivalent samples for each scenario (Table 1, Supplementary Fig. 10, and Supplementary Table 2). We started the simulator from an arbitrary value zero and let mass accumulate or decline indefinitely thus, in effect, permitting us to represent the whole Amazon. From these 10 9 samples of biomass gain or loss we assessed whether the inference of a large carbon sink in old-growth forests is statistically significant 10 , by consulting the t statistic t ¼ dM=dt= s= ffiffiffiffi N p À Á . dM=dt is the trajectory sample mean net carbon balance over 1 year, and s the trajectory sample   30 . We assumed an annual mean mass gain (G) (live tree mass gains plus mass gains due to recruitment 8,10,11 ) of 2.5 Mg C ha À 1 y À 1 in areas of terra firme forests. The simulator of forest mortality (D) is based on the frequency distribution of disturbance area. To convert area losses to biomass losses we assumed a forest mass density of 170 Mg C ha À 1 for all simulations, a high value and B50% greater than the actual biomass density in the lidar landscape in southern Peru used to estimate intermediate disturbance dynamics 8,11 . Assessment of each scenario is based on a set of 10 9 annual equivalent samples. The most credible results are in highlighted bold. *Significance is assessed with a t-test considering t sim ¼ (dM/dt)/(s/sqrt(N)) where dM/dt is ensemble mean mass gain (Mg C ha À 1 y À 1 ), s the s.d. of the mass gain distribution and N the number of observations. For s.d. over the same period. A t-test is justified given the large sample size despite the skewed distributions of net gains, that is, means are indeed nearly normally distributed as predicted by the central limit theorem and tested by Monte Carlo simulations based on the observed distribution of net gains. We run the simulator for various disturbance distribution scenarios to explore the sensitivity of the model to parameter selection. Scenarios with results summarized in Table 1 include three blow-down extents (none, Central Amazon and the full region) and two assumed time-scales (1 and 3.6 year) for detectability of disturbances observed with lidar 24 . Sensitivity to change in growth rates and an extreme-case intermediate-disturbance regime taken from the Peruvian river floodplains are also examined (Supplementary Table 2). The two intermediate-disturbance area cases explore the sensitivity of our results to the spatially biased coverage of the lidar data to one part of the southwest Amazon. The first of the intermediate-scale scenarios use data from terra firme only, the most relevant data for answering our main question because terra firme forests occupy the overwhelming part of the Amazon region. The second extreme intermediate-scale scenario also includes lidar data from flooded forests, which have a greater frequency of larger area disturbance, presumably fluvially induced, although the effect of human disturbance cannot be categorically eliminated because the region studied is affected by extensive unregulated placer gold mining. For small-and large-area disturbances, we did not differentiate geomorphic regimes because they were not apparent in the data.