GoKawiilMoisture tracking in SSPs
We used UTrack, a Lagrangian atmospheric moisture tracking model, to track moisture forwards in time from evaporation to precipitation5,84. Being a three-dimensional Lagrangian tracking model that reconstructs moisture trajectories using evaporation and precipitation directly, UTrack is conceptually similar to some other Lagrangian methods85,86, but differs from other widely used tracking methods that are Eulerian87 or follow changes in specific humidity instead88. Using UTrack, we tracked the three-dimensional atmospheric trajectories of large numbers of individual ‘parcels’ of moisture and updated their positions every time step of 4 h based on evaporation, precipitation, humidity levels and three-dimensional wind speeds and directions. The respective forcing data were output of the medium-resolution Norwegian Earth System Model version 2 (NorESM2)89, which provides sufficiently detailed model output for UTrack and comprises all tier 1 scenarios in ScenarioMIP90 up until 2100: SSP1-2.6, SSP2-4.5, SSP3-7.0 and SSP5-8.5. Furthermore, it outperforms most CMIP6 models on reproducing historical observations of the hydrological cycle91,92. NorESM2 has a temporal resolution of 1 day and a spatial resolution of 1.25° × 0.9375°. We performed forward tracking from each of the 416 grid cells in the Amazon basin for each month and SSP. For each mm of evaporation at each grid cell during each time step of 4 h, we released 100 moisture parcels at random locations above the starting grid cell. Consistent with the ERA5-based UTrack model84, this time step is considerably smaller than the temporal resolution of the forcing data, to prevent skipping of grid cells by parcels during a time step. The wind speeds are calculated for eight pressure levels: 1,000 hPa, 850 hPa, 700 hPa, 500 hPa, 250 hPa, 100 hPa, 50 hPa and 10 hPa. To compensate for underestimated vertical mixing of moisture in the forcing data, each parcel is additionally assigned an occasional quasi-random repositioning along the atmospheric column. This is set such that on average once every 24 h, a parcel repositions itself vertically, where the probability of the new position is weighted by the specific humidity along the column5,84. The moisture content of the parcels is updated if precipitation occurs at that time step in the grid cell corresponding to the position of the parcel and the precipitation moisture is allocated to that grid cell. The tracking and updating continue until 99% of the original moisture in the parcel has been allocated to precipitation or after 30 days have passed since parcel release. It is important to note that, as opposed to ref. 5, we tracked evapotranspiration from each grid cell of the Amazon separately, and stored the results per grid cell, per month and per SSP. As we released 100 parcels per mm of evapotranspiration for each grid cell, this results overall in more than 1 billion parcel releases for this study. As such, although previous studies analysed moisture recycling for the Amazon in CMIP5 (ref. 93) and CMIP6 (refs. 5,94) models, we present grid cell-to-grid cell simulations, enabling us to construct the full moisture flow network. Finally, we validated the NorESM2 wind speed data for the Amazon and the Amazon precipitation recycling ratios using ERA5 reanalysis data and ERA5-forced UTrack runs. We show good correspondence between them and find no systematic bias that can explain our main transition risk results. We present these results in the Supplementary Information (Supplementary Note (Validation of moisture recycling based on EAR5 reanalysis data) and Supplementary Figs. 13–18).
Environmental data
We used MAP and evaporation values (to construct MCWD) from NorESM2 for the adaptation period from 1950 to 2014 (see the ‘Adaptation’ section) as well as for the four SSP scenarios that we used. For the three scenarios SSP2-4.5, SSP3-7.0 and SSP5-8.5, we evaluate the entire century using the now available moisture tracking data (2021–2099) while, for SSP1-2.6, we evaluate the decade 2090–2099 only. MAP and MCWD are computed as 10-year averages to cancel out the effects of single years that are particularly dry or wet. We use 10-year averages to capture long-term climatic shifts that drive system-wide vegetation changes, as supported by rainfall exclusion experiments showing that Amazon forests typically respond to sustained drought conditions over timescales of ten years1,47,65,95. While individual drought years can be impactful, especially for large trees, long-term stress is more relevant for assessing transition dynamics at the basin scale. Moreover, instead of calendar years, we account for dry and wet season conditions by using hydrological years. Hydrological years start in October of one year and run until September of the following year. MAP is computed from adding the corresponding monthly precipitation data in the respective hydrological year. For MCWD, we follow ref. 24 and compute the cumulative water deficit (CWD) from the according monthly precipitation and evaporation values using hydrological years:
$$\begin{array}{rcl} & & {\rm{M}}{\rm{C}}{\rm{W}}{\rm{D}}={\rm{a}}{\rm{b}}{\rm{s}}[\min ({{\rm{C}}{\rm{W}}{\rm{D}}}_{i},{{\rm{C}}{\rm{W}}{\rm{D}}}_{i+1},\ldots ,{{\rm{C}}{\rm{W}}{\rm{D}}}_{i+11})],\\ & & {\rm{w}}{\rm{i}}{\rm{t}}{\rm{h}}\,{{\rm{C}}{\rm{W}}{\rm{D}}}_{i-1}+{{\rm{P}}{\rm{r}}{\rm{e}}{\rm{c}}{\rm{i}}{\rm{p}}{\rm{i}}{\rm{t}}{\rm{a}}{\rm{t}}{\rm{i}}{\rm{o}}{\rm{n}}}_{i}-\,{{\rm{E}}{\rm{v}}{\rm{a}}{\rm{p}}{\rm{o}}{\rm{r}}{\rm{a}}{\rm{t}}{\rm{i}}{\rm{o}}{\rm{n}}}_{i}\\ & & {\rm{a}}{\rm{n}}{\rm{d}}\,\max ({{\rm{C}}{\rm{W}}{\rm{D}}}_{i})=0\end{array}.$$ (1)
Note that we use absolute values of MCWD in this study. While we use monthly precipitation values and evaporation values directly from NorESM2, the resulting global warming levels (from the SSP scenarios) are based on the wider spread of the CMIP6 database to not rely on a single Earth system model and its specific equilibrium climate sensitivity. Specifically, we use the median global temperature change as simulated in MAGICC7 (based on Fig. 4.40a of ref. 96).
Deforestation data
The deforestation data sets are taken from two different data sources. First, we use a severe deforestation data set that originates from ref. 70 and covers the Amazon basin from 2002 to 2050. This scenario assumes that the deforestation trends across the basin continue as well as additional deforestation occurring at locations of (planned) road pavements. At the same time, existing and proposed protected areas are ignored as reasons to limit or stop deforestation at these locations97. The projected deforestation rates were constructed by using historical images and their variations from 1997 to 2002 and then added to the effect of paving a set of major roads. We converted and regridded these data to the same grid as the environmental data, and kept deforestation levels from 2050 constant until the end of the century. From 2020 to 2050, the deforestation increased from ~0.55 million km2 to ~0.9 million km2 in this scenario (that is, from 18% to 35% of the Amazon basin being cleared), leading to an average yearly deforestation of ~18,000 km2 in this period. Despite the fact that the deforestation data are already a bit old, they uniquely project plausible Amazonian deforestation pathways until mid-century, explicitly linked to major infrastructure projects. Thus, the data enable a systematic assessment of critical deforestation thresholds relevant for analysing potential transitions. Second, we also include the deforestation scenarios following the respective SSP-based land use change scenarios (Supplementary Fig. 7). These are conservative scenarios with very limited deforestation after 2020 and none of these scenarios crosses the 25% level of basin-wide deforestation. Furthermore, most deforestation takes place in the west of the Amazon basin rather than in the east where vulnerabilities would be transported downwind.
Adaptation
Forests are not uniformly adapted to local climate conditions54,55,98. Various strategies exist both within and among forests to manage dry seasons and extreme droughts. We assume that local climate conditions have probably driven specific forest trait adaptations through processes such as environmental filtering, competitive exclusion and resilience. Specifically, we assume that forest ecosystems spread throughout the Amazon forest system are adapted to local adaptation values (here on a ~1° × 1° basis). This means that each grid cell is adapted to its past local environmental conditions. Our adaptation period ranges from 1950 to 2014 and includes the consistent historical simulation run, at which the four different SSP scenarios are branched off. Thus, the adaptation period is 1950–2014, while we evaluate the transition risk in the experimental period that ranges from 2021 to 2099 (averaged over a 10-year running average). With adaptation to past local conditions, we mean that the forest cells are adapted to their past MAP and MCWD values in the adaptation period, that is, to local precipitation and drought intensity values. Thus, they represent a local-scale tipping element with a threshold at MAP or MCWD values representing drier conditions than, on average, 1 s.d. away from those in the adaptation period. Locally, this means that critical thresholds can be vastly different; for example, drier regions in the Amazon forest are also capable of surviving drier conditions in the future. Overall, 1 s.d. is a conservative choice as losing 1 s.d. of moisture means on average losing around 25% of its MAP (Extended Data Fig. 4 and Supplementary Fig. 11), or becoming approximately 33% drier (that is, dry season intensity increase; Extended Data Fig. 4 and Supplementary Fig. 11). With this procedure, we are following and extending ref. 45, and follow the hypothesis that safety margins of forest ecosystems to droughts are similar regardless of the present (local) MAP58. However, we also find that our results are robust to the assumption that drier regions have lower safety margins than wetter regions as well as the other way round (see the ‘Robustness checks’ section for details). Lastly, although much of the forest may be adapted to local drought conditions, absolute thresholds are likely to exist for critical transitions in the Amazon forest system1,63 beyond which trees cannot survive. Thus, we ran a robustness analysis taking into account local adaptation as well as discrete thresholds in MAP and MCWD, in which the hard-wired thresholds follow the recent review on critical transitions in the Amazon forest1 with robust results in a qualitative and quantitative sense (see the ‘Robustness checks’ section for details).
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