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Study area and period
Our study area is the tropics between 15°N–35°S6. We divided the study area into three continents and studied them separately: South America, Africa, and Australasia. Australasia includes Australia and southeast Asia, but excludes southern India. Our results are generated on 0.25° spatial resolution. We classify a cell as forest if it contained at least 50% tree cover (‘forest cover’ in this manuscript) in 1999 according to the dataset from ref. 41. The moisture recycling simulations were carried out for 2003–2014 (‘recent climate’), for which a consistent set of input data was available (see also ref. 11). ‘Late 21st century’ refers to 2071–2100.
Local-scale forest hysteresis
Previous research has shown that tropical forests may have local-scale tipping points at certain mean annual rainfall levels, but are also affected by the seasonality of that rainfall5,6,8. Local-scale tipping points for forest were determined using tree cover data following a method from ref. 6. Using potential analysis42, an empirical stability landscape (as in Fig. 1a) is constructed based on spatial distributions of tree cover against environmental variables such as mean annual rainfall for each continent separately. For each value of the environmental variable, the probability density of tree cover was determined using the MATLAB function ksdensity with a bandwidth of 5%. We applied Gaussian weights to the environmental variable with a standard deviation of 0.05 times the length of the axis of the environmental variable. Local maxima of the resulting probability density function are interpreted as stable states, where we ignored local maxima below a threshold value of 0.004. We used Landsat tree cover data for 2000 on 30 m resolution downloaded for every 0.01°43. We masked out human-used areas, water bodies, and bare ground using the ESA GlobCover land cover dataset for 2009 on 300 m resolution (values 11–30 and ≥190). From the resulting dataset we randomly sampled one million locations for each continent and used them to construct the stability landscapes6 against mean annual rainfall and average MCWD. MCWD is the cumulative difference between evapotranspiration and rainfall using monthly averages of those fluxes calculated for each calendar year44. It is set to zero when monthly rainfall exceeds monthly evapotranspiration and becomes more negative with an increasing water deficit. Following ref. 11, for both mean annual rainfall and MCWD, we took monthly data from the GLDAS 2.0 dataset45 for 1970–1999 so the 30-year period leading up to the land-cover sample (for the year 2000) was used.
Forest evapotranspiration
To estimate the fraction of evapotranspiration attributable to forest cover we used the large-scale hydrological model PCR-GLOBWB, run at 0.5° resolution46. Per grid cell, the model simulates evapotranspiration for a range of land-cover types. Here, we are specifically interested in the evapotranspiration of forests, or ‘tall natural vegetation’ in PCR-GLOBWB. Note that we here account for both forest transpiration and canopy interception evaporation instead of, as in ref. 11, only transpiration.
PCR-GLOBWB computes the water balance in two soil layers and a groundwater layer. Soil type, fractional area of saturated soil, and the spatiotemporal distribution of groundwater depth are accounted for (see refs. 46,47). It includes six land-cover types, with spatially varying parameters46: tall and short natural vegetation, pasture, rainfed crops, and paddy and non-paddy irrigated crops. The model was forced with WATCH Forcing Data ERA-Interim precipitation, temperature, and reference potential evapotranspiration for 1979–201448. We used monthly evapotranspiration output of PCR-GLOBWB, implying that we assume that forest component of evapotranspiration remains equal within each month. For detailed model descriptions and validation, we refer to earlier studies11,46,49,50.
Atmospheric moisture tracking
As an essential step in estimating the forest–rainfall feedback, we determined where the moisture from enhanced evapotranspiration precipitates again by using atmospheric moisture tracking. The method for atmospheric moisture tracking resembles that in ref. 11. Apart from the expansion of the study area to the entire tropics, a notable difference is that we here used ERA5 reanalysis data rather than ERA-Interim, meaning that the simulations were based on finer resolution input data (i.e. on 0.25° instead of 0.75° for spatial resolution, and 1 h instead of 3 h for temporal resolution). ERA5 has better performance than ERA-Interim regarding wind fields and rainfall, especially in the tropics51,52,53. Below we summarize the method (see also ref. 11).
We used a Lagrangian method of moisture tracking that is based on previous studies11,54,55,56 that track parcels of evaporated moisture forward through the atmosphere to their subsequent precipitation location. Moisture particles that enter the atmosphere are assigned a random location within the 0.25° grid cell and random starting height in the atmosphere scaled with the humidity profile, and their trajectories are then tracked through the atmosphere. The trajectories are forced with the three-dimensional ERA5 reanalysis estimates of wind speed and direction, which were linearly interpolated at every time step of 0.25 h. Water particles in the atmosphere have an equal probability of raining out, regardless of vertical position. Rainfall A (mm per time step) at location x,y and time t that has evaporated from any location of release in any cell is ref. 56

$$A_{x,y,t} = P_{x,y,t}frac{{W_{{mathrm{parcel}},t}E_{{mathrm{source}},t}}}{{{mathrm{TPW}}_{x,y,t}}},$$
(1)

where P is rainfall in mm per time step, Wparcel is the water in the tracked parcel in mm, Esource is its fraction of water that evapotranspired from the source, and TPW is the precipitable water in the atmospheric water column in mm. Every time step, the amount of water in the parcel is updated based on evapotranspiration ET into the parcel and rainfall P from it:

$$W_{{mathrm{parcel}},t} = W_{{mathrm{parcel}},t – 1} + ({mathrm{ET}}_{x,y,t} – P_{x,y,t})frac{{W_{{mathrm{parcel}},t – 1}}}{{{mathrm{TPW}}_{x,y,t}}}.$$
(2)

The fraction of water in the parcel that has evapotranspired from the source then becomes

$$E_{{mathrm{source}},t} = frac{{E_{{mathrm{source}},t – 1}W_{{mathrm{parcel}},t – 1} – A_{x,y,t}}}{{W_{{mathrm{parcel}},t}}}.$$
(3)

Thus, the amount of water that was tracked from the source location decreases with precipitation along its trajectory. Parcels were followed until either less than 5% of its original amount was left in the atmosphere, or the tracking time was 30 days. Any moisture remaining in the parcel when the trajectories end is assumed to rain out over non-land areas, thus not contributing to our analysis. We analysed each continent separately for reasons of computability. However, small moisture flows between forests in different continents can be expected, as has been simulated for flows from Africa to the Amazon57. Over all land points, ERA5 hourly evapotranspiration is linearly interpolated to every 0.25-h time step. The moisture flow mij in mm per month linking evapotranspiration in cell i to rainfall in cell j where (left[ {x,y} right] , {it{epsilon }} , j) over the course of a given month becomes

$$m_{ij} = mathop {sum}limits_{t = 0}^{{mathrm{month}}} {A_{j,t}} cdot frac{{{mathrm{ET}}_{i,t}}}{{W_{i,t}}},$$
(4)

where ETi,t is the evapotranspiration in mm per time step, and Wi,t is the tracked amount of water from source cell i at time step t.
At continental scales, evaporated moisture can rain down and re-evaporate multiple times. This also means that forest evapotranspiration can enhance rainfall multiple times. We accounted for this ‘cascading moisture recycling’ following refs. 11,14, in which the rainfall attributed to an upwind forest source is subsequently tracked upon re-evaporation. After six re-evapotranspiration cycles, cascading moisture recycling has decreased to practically zero11. Therefore, following ref. 11, seven iterations of cascading moisture recycling were performed.
Hysteresis experiments
We determined the hysteresis of tropical forests through a series of iterative runs; each one started either from a fully forested continent or from a fully deforested continent. We simulated the hypothetical mean annual rainfall levels across the (tropical part of the) continent given this initial condition, that is, rainfall without any forest evapotranspiration or rainfall including evapotranspiration from an entirely forested continent. Next, based on the empirical bifurcation diagrams (i.e. nonforest, bistable forests, and stable forests in each continent are determined based on the bistability ranges shown in Supplementary Figs. 1−3), we determined either the minimal distribution of tropical forest (in case of a no-forest initial condition, based on the higher end of the bistability range) or the maximal distribution (in case of a fully forested initial condition, based on the lower end of the bistability range) at these rainfall levels. Thus, in the simulations with an empty initial condition, only stable forests (green in Fig. 1) would regrow; in those with a full initial condition, both stable and bistable forests (green and yellow in Fig. 1) would disappear. Because the resulting new distribution of forest would generate different levels of rainfall, the procedure was repeated with the respective forest distribution as initial condition. This occurred until rainfall levels had (practically) stabilized between iterative runs (up to three iterations).
We assumed that no other vegetation type replaces the forest in order to show the theoretically possible distributions of tropical forests. This may lead to an overestimation of the actual effects of forest on rainfall, especially if forests would be replaced by highly transpiring crops58. Furthermore, land-cover changes will alter wind patterns and therefore the expected coupling between forests through evapotranspiration and rainfall59. Fossil fuel emissions not only alter the climate, but the emitted CO2 also fertilizes plants. This increases trees’ water-use efficiency, reducing their water demand, but it also increases biomass production60. The effects of this CO2 fertilization on the water cycle might be small61, but its net effects on tropical forest hysteresis remains uncertain.
For display of Fig. 2, the resolution of rainfall values was increased by a factor of 2, to 0.125° and smoothed using a two-dimensional Gaussian kernel with a standard deviation of 0.5°.
Climate-change scenario
As the estimate of late 21st-century rainfall conditions, we used the rainfall output from the SSP5-8.5 scenario simulations by seven available CMIP6 models62. These models are BCC-CSM2-MR, CanESM5, CNRM-CM6-1, CNRM-ESM2, IPSL-CM6A-LR, MRI-ESM2.0, and UKESM1.0-LL. We took the mean across the model outputs for the annual rainfall values for 2071–2100. The scenario is considered a severe climate-change scenario. Because the moisture tracking model is forced with atmospheric reanalysis data, we assumed that (forest-induced) moisture flows in the scenario are the same as in the period of our atmospheric simulations (2003–2014).
We assumed that a tipping point from a forested to a nonforested state occurs when mean annual rainfall in a forested cell (forest cover ≥ 50%) is currently (2003–2014) above the lower tipping point (Supplementary Figs. 1–3), but is reduced to below the lower tipping point in the climate-change scenario. Similarly, a tipping point from a nonforested to a forested state occurs when mean annual rainfall in a nonforested cell (forest cover  More

Scopes and databases
The CEAP dataset comprises all the thermal power plants operating in China, totalling 2,714 plants (or 6,267 units), from 2014 to 2017 in 26 provinces and 4 municipalities (except Hong Kong, Macao, Taiwan and Tibet; Table 1). The thermal power plants produce electricity by combusting a variety of fossil energies, which fall into 4 categories: coal, gas plus oil, biomass and others (detailed in Table 2).
Table 1 China’s thermal power plants in CEAP.
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Table 2 Fuel type descriptions.
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The CEAP dataset integrates two databases, i.e., the CEMS data and unit-specific information. The CEMS data—the direct, real-time measurements of stack gas concentrations of PM, SO2 and NOX from China’s power plant stacks—are monitored by China’s CEMS network and reported to the China Ministry of Ecology and Environment (MEE; http://www.envsc.cn/). The CEMS data are recorded on a source and hourly basis. In total, the CEMS dataset covers 4,622 emission sources (i.e., power plant stacks) associated with 5,606 units (accounting for 98% of China’s thermal power capacity), 35,064 hours from 2014 to 2017, and 3 air pollutants (i.e., PM, SO2 and NOX) for each source-hour sample (Table 3). The MEE has also provided stack-specific information (regarding latitude and longitude, heights, temperature, diameter, etc.; http://permit.mee.gov.cn/).
Table 3 CEMS coverage of China’s thermal power plant units or stacks in CEAP.
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Unit-specific information is also derived from the MEE, involving activity levels (energy consumption and power generation), operating capacities, geographic allocations and pollution control equipment (particularly the types and removal efficiencies) at a yearly frequency. Due to data availability, the unit information is available only until 2016, and the activity levels for 2017 are projected following the overall trends in provincial thermal power generation between 2016 and 2017 (which are available in the China Energy Statistical Yearbooks26), under the assumption that new units constructed in 2017 have the same structures of installed capacities, energy uses and regions as those of the existing units in 2016.
With a combination of the two datasets, the CEAP dataset provides nationwide, plant-level, dynamic PM, SO2 and NOX emissions from China’s thermal power plants from 2014 to 2017. Relative to existing inventories, the CEAP dataset is innovative in that it incorporates comprehensive real CEMS-measured emission data, avoiding the use of average emission factors and the associated operational assumptions and uncertain parameters.
Pre-processing of CEMS data
We have been exclusively granted access to the data from China’s CEMS network. Generally, the CEMS consists of a sampling system (for filtering and sampling flue gas), an online analytical component (for monitoring flue gas parameters, particularly emission concentrations) and a data processing system (for collecting, processing and reporting monitoring data)27,28. According to the GB13223-2003 regulation29, the CEMS network should cover all power plant furnaces that burn coal (except stoker and spreader stoker) and oil and generate >65 tons of steam each hour, as well as those that burn pulverized coal and gas. Thus, some power plants have not yet been incorporated into the CEMS network (accounting for 3–4% of the total thermal power capacity from 2014 to 2017) because their furnaces did not meet the requirements necessary to install a CEMS. For the power plants outside the CEMS network, we assume their stack concentrations are similar to the averages of the units with similar fuel types and similar regions within the CEMS network.
To guarantee the reliability of CEMS data, China’s government has made great efforts in developing specific regulations and technical guidelines for power plants and local entities to follow and supervise, respectively24,28,30,31,32. These official documents elaborate on all the processes required to regulate the CEMS network, including not only CEMS installation, operation, inspection, maintenance and repair but also CEMS data collection, processing, reporting, analysis and storage28,32,33. Since 2014, all state-monitored companies have been mandated to report their CEMS data to the local governments through a series of online platforms for different provinces (listed in Supplementary Table 1). Local entities have random onsite inspections to check the truthfulness of the reported results on at least a quarterly basis23,24,28,32,34; this system enables a comparison of CEMS data across different firms to explore potential outliers and abnormalities and prevent data manipulation28,35. Then, the governments release the inspection results to the public through the same online platforms (listed in Supplementary Table 1)24,36,37. Severe financial penalties and criminal punishments can be imposed on firms that adopt data manipulation (in terms of deleting, distorting and forging CEMS data, for example)38,39.
The malfunction of CEMS monitors may also introduce large uncertainty to CEMS data during the processes of operation (indication errors, span drift, zero drift, etc.), maintenance (particularly the failure to perform calibration and reference tests) and data reporting (invalid data communication, data missing, etc.)24,28. Accordingly, each power plant is required to make at least one A-, B- and C-grade overhaul for 32–80, 14–50 and 9–30 days per 4–6, 2–3 and 1 year(s), respectively, as well as one D-grade overhaul (if needed) for 5–15 days per year, to check, maintain and upgrade its technologies, thereby reducing measurement uncertainty40. During these overhauls, CEMS operators conduct CEMS calibration (i.e., zero and span calibration), maintenance procedures (e.g., examining and cleaning major CEMS components and replacing or upgrading parts, if necessary, such as optical lens, filter and sampling meter) and a reference test (i.e., relative accuracy test audit). Furthermore, third-party operators examine CEMS operation and maintenance routines, to guarantee standardized CEMS operation and facilitate improvement in CEMS data accuracy27,28,31. All the related activities should be documented according to standardized requirement contents27,28. Even with the aforementioned efforts, there is still a small proportion of nulls and outliers in the CEMS database, which represent 1% and 0.1% of the total operating hours, respectively, from 2014 to 2017. We treat these samples seriously by following the relevant official documents, which have been released by China’s government. Table 4 provides the treatment methods for nulls or zeros, which can be divided into 3 types based on duration. On the one hand, we consider nulls and/or zeros that span at least 5 successive days as a downtime or overhaul and omit them in the estimation, according to the regulation27. On the other hand, missing data lasting  24 hours are assumed around the valid values near the time and set to the monthly averages27:

$${hat{C}}_{s,i,y,m,h}={bar{C}}_{s,i,y,m,bullet }$$
(1)

where ({C}_{s,i,y,m,h}) denotes the stack gas concentrations of pollutant s emitted by unit i for year y, month m and hour h (i.e., the actual measurements monitored by the CEMS network), defined as the amount of pollutants per unit of emitted stack gas (g m−3)41,42; ({widehat{C}}_{s,i,y,m,h}) is the imputation for the missing data ({C}_{s,i,y,m,h}); ({bar{C}}_{s,i,y,m,.}) is the mean of the hourly valid values for the same pollutant, unit, year and month as ({C}_{s,i,y,m,h}). In contrast, the missing data for 1–24 hour(s) are interpolated with the arithmetic averages of the two nearest valid points before and after them27,43:

$${widehat{C}}_{s,i,y,m,h}=frac{{C}_{s,i,y,m,h-l}+{C}_{s,i,y,m,h+q}}{2}$$
(2)

where ({C}_{s,i,y,m,h-l}) and ({C}_{s,i,y,m,h{rm{+}}q}) represent the nearest last known measurements (l hour(s) before) and next known measurements (q hour(s) after), respectively, for the missing data ({C}_{s,i,y,m,h}), namely, the series data ({C}_{s,i,y,m,h-l+1}),…, ({C}_{s,i,y,m,h}),…, ({C}_{s,i,y,m,h+q-1}) are all missing values. Furthermore, we treat the measurements that are out of the measurement ranges of CEMS instruments (outside of which the data are unreliable30,44; detailed in Supplementary Table 2) as abnormal data and process them in a similar way to nulls according to the official regulation27.
Table 4 Treatment methods for nulls and the relevant official documents.
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CEMS-based estimation of emission factors and absolute emissions
The introduction of real CEMS-monitored measurements provides a direct estimation for emission factors on a source and hourly basis, avoiding the use of average emission factors with many assumptions and uncertain parameters17,42,44.

$$E{F}_{s,i,y,m,h}={C}_{s,i,y,m,h}{V}_{i,y}$$
(3)

In Eq. (3), (E{F}_{s,i,y,m,h}) indicates the emission factor, defined as the amount of emissions per unit of fuel use (in g kg−1 for solid or liquid fuel and in g m−3 for gas fuel), and ({V}_{i,y}) is the theoretical flue gas rate, defined as the expected volume of flue gas per unit of fuel use under standard production conditions (m3 kg−1 for solid or liquid fuel and m3 m−3 for gas fuel)42, which was estimated by the China Pollution Source Census (2011)45 based on sufficient field measurements (detailed in Table 5). Based on Eq. (3), abated emission factors can be directly obtained even without the use of removal efficiencies and the relevant parameters, because CEMS monitors the gas concentrations at stacks after the effect of control equipment (if any).
Table 5 Theoretical flue gas rate.
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Notably, recent clean air policies (particularly different emissions standards) target stack concentrations, such that a large proportion of missing data exist regarding other measurements (particularly flue gas rates, with missing data accounting for 34.62%, 31.91%, 29.97% and 42.96% of the total samples in 2014, 2015, 2016 and 2017, respectively). Accordingly, we introduce theoretical flue gas rates into the estimation to avoid significant underestimation of the actual volume when there are too many missing data values46. In addition, the adoption of theoretical flue gas rates can address flue gas leakage, a common problem in power plants that greatly distorts the real flue gas volume46. The theoretical flue gas rates are derived from the China Pollution Source Census, with values varying across operating capacities, fuel types and boiler types42,45. Thus, the actual volume of flue gas is computed in terms of the theoretical flue gas rate times actual fuel consumption.
The absolute emissions of PM, SO2 and NOX from individual power plants can be estimated in terms of the emission factors times the activity levels21:

$${E}_{s,i,y,m}=E{F}_{s,i,y,m}{A}_{i,y,m}$$
(4)

where ({E}_{s,i,y,m}) represents the air pollution emissions (g); and ({A}_{i,y,m}) is the activity data, i.e., the amount of fuel use (kg for solid or liquid fuel and m3 for gas fuel). In the CEAP dataset, power plant emissions are estimated on a monthly basis (the smallest scale for activity data), in which the yearly unit-level activity data are allocated at the monthly scale using the monthly province-level thermal power generation as weights16:

$${A}_{i,y,m}=frac{{F}_{{p}_{i},y,m}}{{sum }_{m=1}^{12}{F}_{{p}_{i},y,m}}{A}_{i,y}$$
(5)

where ({F}_{{p}_{i},y,m}) denotes the thermal power generation by province Pi, which is obtained from the Chinese Energy Statistics Yearbook26, and ({p}_{i}) indicates the province where unit i is located. More

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