Estimating the spatial amplification of damage caused by degradation in the Amazon

Abstract

The Amazon rainforests have been undergoing unprecedented levels of human-induced disturbances. In addition to local impacts, such changes are likely to cascade following the eastern-western atmospheric flow generated by trade winds. We propose a model of spatial and temporal interactions created by this flow to estimate the spread of effects from local disturbances to downwind locations along atmospheric trajectories. The spatial component captures cascading effects propagated by neighboring regions, while the temporal component captures the persistence of local disturbances. Importantly, all these network effects can be described by a single matrix, acting as a spatial multiplier that amplifies local forest disturbances. This matrix holds practical implications for policymakers as they can use it to easily map where the damage of an initial forest disturbance is amplified and propagated to. We identify regions that are likely to cause the largest impact throughout the basin and those that are the most vulnerable to shocks caused by remote deforestation. On average, the presence of cascading effects mediated by winds in the Amazon doubles the impact of an initial damage. However, there is heterogeneity in this impact. While damage in some regions does not propagate, in others, amplification can reach 250%. Since we only account for spillovers mediated by winds, our multiplier of 2 should be seen as a lower bound.

Keywords: Amazon rainforests; cascading effects; degradation; spatial–temporal autoregression.

Fig. 1.

Mechanism and model. This figure illustrates the mechanism behind changes in forest vegetation and degradation. An initial forest status is perturbed by shocks (deforestation or droughts, for example). The shock will change the forest status, changing transpiration and thus atmospheric moisture. Atmospheric moisture is transported by atmospheric trajectories affecting the amount of rainfall in downwind regions. The change in downwind rainfall affects degradation processes that determine a new forest status. The statistical model abstracts from the transpiration mechanism and uses variations in atmospheric trajectory to estimate the dynamics of the forests.

Fig. 2.

Data and estimates. Data showing (A) the average Leaf Area Index for the year 1985 (LAI) representing local forest status, and (B) atmospheric transport, calculated as the 5-d back trajectories for a sample of our pixels. (C) estimated spatial lags (${\beta }_k$) for each $k$ between 1 and 20. The shaded gray area shows the 95% CI with SEs clustered at the pixel level.

Fig. 3.

Index of influence (A) and index of exposure (B). (A) The total effect that a shock in a pixel has accounting for all the spatial feedbacks. Each entry $\mathrm{\Omega }(i,j)$ represents the effect that pixel $j$ has on pixel $i$. For each pixel, represented by a column of $\mathrm{\Omega }$, the map shows the sum of values in that column. This sum measures the effect of the pixel on the entire forest. (B) The total effect that a pixel receives accounting for all the spatial feedbacks. For each pixel, represented by a row of $\mathrm{\Omega }$, the map shows the sum of values in that row; this sum measures the potential of that pixel to be affected by the entire forest. The maps are colored according to the quartiles of the effects; that is, it shows the distribution from the 25% smallest multiplier effects (blue) to the 25% largest ones (yellow). The histogram below each map shows the distribution of the multiplier effects.

Fig. 4.

These maps show the following: The pixels that were most deforested between 2001 and 2022 (the white squares in A and B) (42). We selected pixels that were deforested more than 50%. Together, those pixels represent 32% of the total deforestation in the Amazon; we then map the areas that are affected by the deforestation in the white pixels (the values on the columns of $\mathrm{\Omega }$ corresponding to the white pixels). To facilitate visualization, we break down the affected pixels into bins (10% to 15%, 15% to 20%, and $>$20%) where each bin represents the share of the change in LAI in the white pixels that will be propagated. Map B shows a zoomed-in version of map A, in the arch of deforestation in Brazil.