Assessing the impacts of past and ongoing deforestation on rainfall patterns in South America

Despite recent advances in modeling forest–rainfall relationships, the current understanding of changes in observed rainfall patterns resulting from historical deforestation remains limited. To address this knowledge gap, we analyzed how 40 years of deforestation has altered rainfall patterns in South America as well as how current Amazonian forest cover sustains rainfall. First, we develop a spatiotemporal neural network model to simulate rainfall as a function of vegetation and climate inputs in South America; second, we assess the rainfall effects of observed deforestation in South America during the periods 1982–2020 and 2000–2020; third, we assess the potential rainfall changes in the Amazon biome under two deforestation scenarios. We find that, on average, cumulative deforestation in South America from 1982 to 2020 has reduced rainfall over the period 2016–2020 by 18% over deforested areas, and by 9% over non‐deforested areas across South America. We also find that more recent deforestation, that is, from 2000 to 2020, has reduced rainfall over the period 2016–2020 by 10% over deforested areas and by 5% over non‐deforested areas. Deforestation between 1982 and 2020 has led to a doubling in the area experiencing a minimum dry season of 4 months in the Amazon biome. Similarly, in the Cerrado region, there has been a corresponding doubling in the area with a minimum dry season of 7 months. These changes are compared to a hypothetical scenario where no deforestation occurred. Complete conversion of all Amazon forest land outside protected areas would reduce average annual rainfall in the Amazon by 36% and complete deforestation of all forest cover including protected areas would reduce average annual rainfall in the Amazon by 68%. Our findings emphasize the urgent need for effective conservation measures to safeguard both forest ecosystems and sustainable agricultural practices.

critical. In recent decades, numerous studies, particularly in the Amazon, have greatly improved our understanding of how deforestation leads to changes in rainfall patterns (e.g., Salazar et al., 2015;Spracklen & Garcia-Carreras, 2015;Staal, Flores, et al., 2020). These studies were partly motivated by the ongoing forest loss in South America especially in Brazil (Amigo, 2020;Kalamandeen et al., 2018;Souza et al., 2020). For example, Brazil has lost an estimated 50 million hectares (11.3%) of the Amazon rainforest and 27.5 million hectares (20%) of native vegetation in the Cerrado between 1985 and 2021 (Curtis et al., 2018;Souza et al., 2020). While these studies are useful for understanding the mechanisms by which large-scale deforestation affects rainfall patterns, they do not necessarily reflect the complexity of real-world deforestation processes and their cumulative effects over time especially at the continental scale. However, there are a few notable studies, such as Khanna et al. (2017), that have captured the relationship between small-scale deforestation and changes in rainfall patterns at the subnational scale.
In this study, we analyze the cumulative impacts of historical deforestation (i.e., between 1982 and 2020) on rainfall patterns across South America. We pay particular attention to capturing both local and remote effects to provide a broader picture of the complex interactions between deforestation and rainfall patterns, accounting for the diverse range of deforestation processes and their spatiotemporal dynamics. Specifically, we assess the spatial impacts of deforestation on various aspects of rainfall, including magnitude, relative entropy, dry season length, and dry season intensity.
Furthermore, we project the potential effects of future deforestation on rainfall patterns both inside and outside protected areas in the Amazon biome, given the high vulnerability of unprotected areas to land-use conversion. To accomplish this, we utilize a spatiotemporal neural network modeling approach to capture spatial patterns and dependencies between grid cells, as well as recurrent connections to capture temporal patterns and dependencies between grid cells over time. We analyze the effects of different types of past deforestation, such as commodity-driven deforestation (CDD) and shifting agriculture-driven deforestation (SAG), to provide a more nuanced understanding of the problem. This study builds upon and enhances a previously deployed data-driven modeling approach that used input data from Sub-Saharan Africa (Duku & Hein, 2021).

| ME THODOLOGY
Our methodology consists of three steps: (i) development of a spatiotemporal neural network model, that we name 'DeepRainForest', which predicts daily rainfall as a function of climate and vegetation inputs; (ii) assessment of the effects of historical deforestation during the periods 1982-2020 and 2000-2020 on rainfall patterns; and (iii) prediction of potential rainfall changes assuming deforestation continues in the Amazon biome. By analyzing the effects of past deforestation on rainfall in two time periods, we are able to disentangle the effects of recent deforestation (i.e., 2000-2020) from the effects of long-term deforestation (i.e., 1982-2020).

| Developing the DeepRainForest model
We developed the DeepRainForest model to predict daily rainfall across South America as a function of daily wind speed and direction, air pressure on the surface of the earth (ERA5 Reanalysis, Hersbach et al. (2020)), sea-surface temperature (Reynolds & Banzon, 2008), fractional tree and herbaceous cover (DiMiceli et al., 2021), leaf area index (LAI; Myneni et al., 2015), and black sky albedo for the near infrared broadband (Schaaf & Wang, 2015). The selection of these variables was based on an extensive review of the existing literature (e.g., Ellison et al., 2017;Spracklen et al., 2018). We obtained all climate data from reanalysis sources (ERA5 Reanalysis, Hersbach et al. (2020)) at a spatial resolution of 0.25 decimal degrees. Reanalysis data provide a comprehensive and consistent dataset that combines various observations and models to reconstruct past climate conditions and are widely used to understand the forest-rainfall relationship (e.g., Staal et al., 2018;. In addition, vegetation data were acquired from satellite measurements (DiMiceli et al., 2021;Myneni et al., 2015;Schaaf & Wang, 2015).
To align the spatiotemporal resolutions of climate and vegetation data, tree cover, herbaceous cover, and LAI data were temporally downscaled to daily time-steps using Fast Fourier transform (Virtanen et al., 2020). All vegetation data were then regridded to 0.25 decimal degrees to align with the spatial resolution of climate data. The DeepRainForest model is based on the Convolutional Long-Short Term Memory (ConvLSTM) neural network. The ConvLSTM is a type of recurrent neural network, which has the capacity to learn long-term dependencies between response and predictor variables and preserve the three-dimensional structure of spatiotemporal data sequences (Shi et al., 2015).
ConvLSTM layers, like LSTMs, consist of memory cells and three self-parameterized gates that regulate information flow.
Equations (1-6) provide a general description of a ConvLSTM layer according to (Xingjian et al., 2015). Memory cells, represented as C t , gather information from input data over extended periods of time.
The forget gate, f t , decides which information should be discarded from the previous cell state, C t−1, . The input gate, i t , in conjunction with a tanh layer, g t, , updates the previous cell state. The input gate determines which information from the previous cell state, C t−1, should be updated, while the tanh layer decides which candidate information from the current input data, X t , and the previous output/ hidden state, H t−1 , should be added to the memory cell. The output gate, o t , determines which information from the current cell state, C t , should be propagated to the current hidden state, H t , and therefore, become a candidate for accumulation in the cell state during the next sequence. The input, forget, and output gates are made up of sigmoid functions, , with values ranging from 0 to 1, that regulate the amount of information passing through the gates. For instance, if f t equals 0, the model discards all information stored in the previous cell state, and if it equals 1, it retains all previous information. W represents the weight, which indicates the strength of connection between units in each layer, and b is the bias, which is similar to a constant in a linear function. The symbol ⊙ represents an elementwise dot product, and * indicates the convolution operator.
The DeepRainForest network architecture consists of four stacked ConvLSTM layers, which are interposed between two stacked convolutional layers and two stacked transposed convolutional layers. The presented architecture allows for capturing local and remote effects of vegetation changes on rainfall by utilizing convolutional filters to capture spatial patterns and dependencies between grid cells, as well as recurrent connections to capture temporal patterns and dependencies over time. The stacking of multiple layers of convolutional filters in the network architecture, allows the network to capture spatial dependencies at multiple scales. The detailed neural network architecture is presented in Figure S1. This current version is an enhancement of a model that we previously deployed across Sub-Saharan Africa (Duku & Hein, 2021). Compared to the prior version, this current version operates at a higher spatial resolution (i.e., 0.25 decimal degrees), incorporates additional vegetation data (i.e., albedo and fractional herbaceous cover) and adds sea-surface temperature data. Sea-surface temperature in the Atlantic and Pacific oceans are strong modulators of the regional climate in South America influencing weather patterns, precipitation, and atmospheric circulation. Albedo represents the reflectivity of land surfaces and plays a crucial role in the energy balance and feedback processes within the Earth's climate system.
The DeepRainForest model was trained on daily time series of input data and ERA5 rainfall data (Hersbach et al., 2020)

| Quantifying the impacts of past and future deforestation on rainfall
To investigate the impact of historical deforestation on rainfall patterns, specifically focusing on CDD and SAG, we identified deforestation hotspots ( Figure 1) associated with these drivers based on F I G U R E 1 Deforestation hotspots and their underlying drivers, adapted from Curtis et al. (2018). All colored areas are deforestation hotspots between 2001 and 2015, categorized as follows: Commodity-driven deforestation (CDD) which represents areas where forest loss and deforestation are driven by commodity production characterized by long-term, permanent conversion of forest and shrubland to a nonforest land use such as agriculture; shifting agriculture (SAG) which represents areas where forest loss is driven by small-to medium-scale forest and shrubland conversion for agriculture that is later abandoned and followed by subsequent forest regrowth; forestry (FOR) which represents areas where forest loss is driven by large-scale forestry operations occurring within managed forests and tree plantations with evidence of forest regrowth in subsequent years. For each indicated point, the time-series subplots depict the tree cover from 2001 to 2020. data from Curtis et al. (2018) and performed controlled simulations by maintaining tree cover and vegetation data in these hotspots constant at 1982 and 2000 levels. The data from Curtis et al. (2018) represent aggregated forest loss occurrences with attribution to specific drivers. However, it is important to note that these data do not account for medium-to long-term forest cover dynamics. As a result, areas with a generally increasing forest cover trend, despite few instances of recorded forest loss, were also included in the delineated deforestation zones. For our analysis, we did not consider such areas as hotspots of forest loss. To eliminate such areas from the data, we tested annual tree cover data between 2001 and 2020 for trends using Mann Kendall trend test. Grid cells that had been designated as deforestation hotspots by Curtis et al. (2018) and that overlapped with areas with statistically significant (p < .1) positive trend in tree cover were then eliminated and not used in For all simulations, that is, with and without historical deforestation, we computed and compared the rainfall magnitude, relative entropy, dry season length, and dry season intensity. Rainfall magnitude is the annual rainfall total. Relative entropy is a thresholdindependent information theory measure that quantifies the extent of annual rainfall concentration (Feng et al., 2013). It ranges from 0 to 3.6, with a value of 0 indicating uniform monthly rainfall distribution throughout the year and 3.6 indicating that annual rainfall is concentrated in only 1 month. Dry season length is the number of months where mean monthly rainfall is less than mean monthly potential evapotranspiration (Aragão et al., 2007). Monthly estimates of potential evapotranspiration were obtained from Abatzoglou et al. (2018). The original dataset was at a spatial resolution of 2.5 arc-minute and was subsequently regridded to 0.25 decimal degrees. The potential evapotranspiration was computed using the Penman Montieth approach (Allen et al., 1998). Dry season intensity is the total cumulative water deficit during dry months (Aragão et al., 2007). Rainfall magnitude, R k ; relative entropy, D k ; dry season length, DSL; and dry season intensity, DSI, were calculated using Equations (7-11), where the associated monthly rainfall distribution, p k,m , and the relative entropy, D k are computed from the monthly total rainfall r k,m and where q m is the uniform distribution, for which each month has a value of 1/12; m is the number of months in the year; p m is the mean monthly rainfall for month m; and PET m is the mean monthly potential evapotranspiration for month m.
To better understand the relation between forest cover and rainfall in the Amazon biome, we conducted two additional assessments.
First, we examined the effects of complete tree cover loss outside F I G U R E 2 Leaf area index (LAI) (a) and albedo (b) profiles used as input for the control simulations. LAI and albedo profiles were derived for different tree cover intervals based on data from 2001 to 2020.
of protected areas ( Figure S2), which would be a rather extreme, but not entirely unthinkable scenario for future tree cover decline.
Data from UNEP-WCMC and IUCN (2022) were used to delineate the protected areas ( Figure S2). Second, we looked at the impact of complete tree cover loss in the entire Amazon biome in order to illustrate the overall importance of forest cover for maintaining rainfall patterns. As inputs to our partial and complete deforestation simulations, the LAI and albedo profiles of each respective tree cover scenario were derived following the approach earlier described in this section (Figure 2).

| DeepRainForest model performance assessment
Our model is able to reproduce the spatiotemporal pattern of rainfall with high accuracy (Figure 3). On a daily time-step, the DeepRainForest model (Figure 4) achieves NSE and Kendall tau correlation coefficients greater than 0.5 over large areas especially over forested regions such as the Brazilian Amazon, Mata Atlantica, the F I G U R E 3 Comparison of observed (ERA5) and mean monthly spatial rainfall patterns predicted by DeepRainForest from January (a) to December (l) over the validation period, that is, 2014-2018.
Chilean temperate forest areas as well as the Cerrado region (4a).
For monthly time-step, the NSE and Kendall tau coefficients increase substantially over the aforementioned forested regions and the Cerrado to over 0.75 (4b), indicating the accuracy of our model for several biomes. Over these areas the model on average tends to overestimate both daily and monthly rainfall prediction. This can be attributed to the high frequency of dry days, that is, days with 0 mm of rainfall. For a substantial portion of these days, our model tends to predict rainfall. The rainfall predicted by the model for these days is mostly less than 1 mm and negligible in absolute terms. However, for such a pairwise comparison it tends to affect the outcome. A comparison of ERA5 rainfall and simulated rainfall for selected grid cells is shown in Figure S3.

| Impacts of historical deforestation on observed rainfall pattern
Historical deforestation in South America has substantially affected both local and regional rainfall patterns. As a result of cumulative effects, we find that the deforestation-induced changes in rainfall pattern are much more pronounced over recent years (2016-2020, which represent the last 5 years of the simulation period) than in earlier years. Hence, unless specified otherwise in this section, the changes in rainfall that we describe are for the 2016-2020 period. Over deforestation hotspots delineated in this study, we find that the mean annual rainfall would have been 18% higher without the deforestation that occurred between 1982 and 2020 ( Figure 5), and it would have been 10% higher without deforestation between 2000 and 2020 ( Figure 6). Over areas not delineated as deforestation hotspots and where vegetation cover remained the same for all simulations, we find that the mean annual rainfall would have been 9% higher without deforestation in delineated hotspots between 1982 and 2020. It would have been 5% higher without deforestation between 2000 and 2020.
These findings clearly show that deforestation does not only affect local rainfall but also rainfall in nearby or remote areas.
Much of the reduction in rainfall experienced due to deforestation is concentrated in the Amazon, Cerrado, and Caatinga biomes where substantial tree cover has been lost over the past four decades. For instance, in the Amazon biome, mean tree cover was reduced from about 82% in 1982 to less than 62% in 2020 ( Figure 7a).
As a result, 50% of the Amazon biome recorded a mean annual rainfall exceeding 1800 mm year −1 whereas, without recorded deforestation between 1982 and 2020, 75% of the Amazon biome would have exceeded this amount (Figure 7b). In the Cerrado, about 25% of the area recorded mean annual rainfall of exceeding 1300 mm year −1 , whereas without recorded deforestation between 1982 and 2020, 70% of the biome would have exceeded this amount.
We also find that historical deforestation has increased the relative entropy of rainfall especially in the Amazon-Cerrado frontier indicating that rainfall is concentrated in fewer months than would have been the case without historical deforestation (Figure 5d-f).
Over the Amazon-Cerrado frontier, rainfall is concentrated in the November to May period. An increase in relative entropy indicates that without historical deforestation, rainfall magnitude would have been higher and would have been spread over more months than is currently the case. Over the Amazon biome, 40% of the area currently has a minimum relative entropy of 0.2 whereas without deforestation recorded between 1982 and 2020 this would have been 25% of the area (Figure 7c). In the Cerrado biome, 50% of the area currently has a minimum relative entropy of 0.4 whereas without deforestation between 1982 and 2020 this would have been 15% of the area. Generally, because of cumulative effects, deforestation in the period 1982-2020 had greater negative impact on rainfall than in the period 2000-2020 (Figure 8).
To understand the societal impacts of deforestation-induced droughts or dry season changes, it is important to assess if the remaining rainfall is sufficient to satisfy crop or vegetation water demand. We used potential evapotranspiration as a measure of crop and vegetation water demand. Our findings show that dry season length, that is, the number of months when rainfall is less than potential evapotranspiration, has increased substantially over deforestation hotspots especially in the Amazon and the Cerrado and to a lesser extents over remote areas. Currently about 60% of the Amazon biome F I G U R E 5 Changes in rainfall pattern averaged over the period 2016-2020 as a result of cumulative deforestation from 1982 to 2020. Estimated changes in rainfall magnitude (a-c); relative entropy (d-f); dry season length (g-i); and dry season intensity (j-l). Negative values indicate reduction as a result of deforestation and positive values indicate increase.
has at least 4 months where total precipitation is less than potential evapotranspiration. However, without deforestation between 1982 and 2020, this would have been only 25% of the area (Figures 5g-i   and 7d). For the Cerrado, currently about 50% of the biome experience dry seasons of at least 7 months, whereas without deforestation only about 20% would have experienced a dry season of this duration (Figures 5g-i and 7d). Our findings also suggest that dry season duration has not only increased but, in addition, water deficit within these months have intensified (Figures 5j-l and 7e). Because potential evapotranspiration over a specific grid cell is unaffected by deforestation, increasing water deficit can be attributed to deforestationinduced changes in rainfall. We connected the change in rainfall to the different drivers for deforestation based on Curtis et al. (2018), and found that the rainfall pattern changes revealed in our analysis have been caused largely by CDD whereas in the Caatinga it is driven largely by shifting agriculture (SAG) (Figures 5 and 6).

| Potential impacts of further deforestation on rainfall
Over the Amazon biome, the conversion of all forest cover outside protected areas to pasture would reduce rainfall magnitude substantially. Some areas would lose as much as 80% or more of annual F I G U R E 6 Changes in rainfall pattern averaged over the period 2016-2020 as a result of cumulative deforestation from 2000 to 2020. Estimated changes in rainfall magnitude (a-c); relative entropy (d-f); dry season length (g-i); and dry season intensity (j-l). Negative values indicate reduction as a result of deforestation and positive values indicate increase. rainfall ( Figure 9). Over deforested areas, mean annual rainfall is likely to be reduced by about 48% in the Amazon biome whereas over non-deforested areas this would be 26%. Across the amazon biome, conversion of forest cover outside protected areas would reduce average annual rainfall by 36% and conversion of all forest cover including protected areas would reduce average annual rainfall by about 68%.

| D ISCUSS I ON AND CON CLUS I ON S
Our paper advances the current knowledge of forest-rainfall re- to soybean crops (Song et al., 2021 We note that impacts of future deforestation are, in particular, prone to uncertainty including from threshold effects in ecosystem responses (e.g., Ratajczak et al., 2018). A number of studies with global climate models that incorporate various levels of deforestation suggest that tropical forest clearing beyond ∼30%-50% may constitute a critical threshold for the Amazon, beyond which reduced rainfall triggers a significant decline in ecosystem structure and function (Lawrence & Vandecar, 2015). Even though our study confirms that major changes in rainfall magnitude and dry season length are likely to occur in case large areas would be deforested, we did not investigate the specific threshold below which deforestation in the Amazon leads to an abrupt change in rainfall. We note that there are several other feedback mechanisms in the ecosystem that we did not include in our model and that could accelerate rainfall changes compared to our model outcomes. For instance, reduced rainfall may increase fire risks (Hoffmann et al., 2003;Holden et al., 2018) that may cause further reductions in forest cover. Since we do not consider such feedbacks in our analysis, we may underestimate the effects of deforestation on rainfall patterns. We also note that such dynamics may be subject to hysteresis, that is, restoring rainfall patterns may well require forest cover to be restored to a higher density compared to the threshold where threshold effects first occurred.
Our findings clearly show past deforestation has negatively affected rainfall patterns over deforested areas as well as nondeforested areas especially in the Amazon-Cerrado agricultural frontier. These changes in rainfall patterns have had and will continue to have severe agronomic and economic implications that urgently need to be acknowledged in agrobusinesses and in policy making. Reductions in rainfall immediately impact agricultural yields given that rainfall is already a major constraint to agricultural productivity in parts of the Amazon and much of the Cerrado biome (e.g., Lawrence & Vandecar, 2015;Leite-Filho et al., 2021).
Hence, there is a critical trade-off at play. Converting forest to cropland and pastures increases land available for agriculture, but at the same time reduces yields across existing and new croplands and pastures. This trade-off is not yet well understood, and there is an urgent need for further work to inform policy making how far Brazil is removed from the point where converting additional land to cropland and pastures actually reduces economic outputs.
These effects will not be uniformly spread across the Amazon: our findings show that the relative impacts on rainfall are highest in the Southern arch of the Amazon (see Figures 5 and 6), yet the impacts on crop production may be highest in areas with currently a low rainfall compared to the needs of the main crops, in particular Bahia state. Furthermore, policy making should consider that the forest-rainfall relationship is prone to uncertainty and that critical thresholds exist which, together with teleconnection effects, may cause the rainfall system to collapse quicker than is indicated by the current projections.

CO N FLI C T O F I NTE R E S T S TATE M E NT
The authors have no conflicts of interest to declare.

DATA AVA I L A B I L I T Y S TAT E M E N T
The data that support the findings of this study are openly available in Zenodo at https://doi.org/10.5281/zenodo.8071547.