Many studies have suggested that the Amazon rainforest may be a potential tipping element of the earth system1,2. Results of several coupled global climate models have indicated the possibility of a future dieback of the rainforest under global warming scenarios3,4, but also ongoing deforestation has been discussed as a possible cause of a regime shift of the ecosystem5,6,7,8,9,10,11,12. Here, we propose a model of the nonlinear couplings between the atmospheric moisture transport over South America and the Amazon rainforest, which are associated with a westward cascade of precipitation and evapotranspiration. Impacts of ongoing deforestation on the South American low-level circulation will be analyzed with particular focus on a positive atmospheric feedback induced by condensational latent heat release over the Amazon13,14,15, which is neglected in most studies investigating the consequences of deforestation on the resilience of the Amazonian rainforest.

Rainfall in vast parts of South America critically depends on the atmospheric moisture inflow from the tropical Atlantic ocean. After crossing the Amazon basin, these moist low-level winds are blocked by the Andes mountains to the west and channelled southwards, forming a low-level jet from the western Amazon basin to the subtropics, for which it is the most important moisture source16.

Due to the release of latent heat (LH), precipitation over tropical South America strengthens the atmospheric heating gradient between the Atlantic ocean and the continent, and thereby enhances the low-level atmospheric inflow into the Amazon basin. This heating gradient can be estimated to enhance the easterly inflow into South America by a factor between 2 and 3 during the monsoon season (December–February)13,14,15. The Amazon rainforest’s evapotranspiration (E) recharges the low-level atmosphere’s moisture content, resulting in additional moisture being available for precipitation (P) further downstream of the westward flow. In turn, high P rates and the associated condensational heating are crucial for the existence of the rainforest itself, and thus for maintaining high E rates in the long term. Due to these feedback mechanisms, widespread deforestation does not only impact the ecosystem locally, but may cause nonlinear responses of the atmospheric circulation regime, and thereby impact climate in other regions as well1. In particular, the easterly low-level flow across the Amazon basin will cause the impacts of deforestation in terms of available moisture and LH release to cascade westward to yet undisturbed parts of the rainforest and further downstream toward the subtropics. For example, a recent study estimates that as much as 70% of P in the La Plata basin, a region with extensive agricultural activity17, originate from E in the Amazon basin18.

Most existing studies investigate the impacts of deforestation in the Amazon basin by comparing model results obtained from scenarios with intact rainforest to results obtained from scenarios where the rainforest is completely removed5,8,19,20. While this is certainly useful for assessing the climatological relevance of the Amazonian ecosystem, it is less helpful to understand the specific ways in which ongoing deforestation will successively affect the biosphere-atmosphere couplings in terms of moisture recycling and condensational LH release. In contrast, two recent studies9,21 based on general circulation models (GCMs) analyse impacts of successive deforestation on P, and find that P decreases weakly nonlinearly as deforestation proceeds. However, the first9 only investigates impacts on P over the eastern Amazon basin, although the cascading effects of deforestation in the eastern Amazon can be expected to be more severe in the western regions, further downstream of the low-level flow. The latter21 does not analyse the atmospheric mechanisms causing the nonlinearities. Furthermore, such GCM-based studies are based on single realisations of the multitude of possible parameters used in the GCM equations. The huge uncertainties associated with these parameter choices can in general hardly be estimated in a rigorous way22. For example, projections of the future fate of the Amazon vary substantially between different GCMs, and even from one version of a single GCM to the next23. The sensitivity of P over the Amazon basin against small variations of the relevant parameters, such as deforestation-induced changes in surface net radiation and the heating gradient between ocean and land, cannot be investigated along those lines. However, knowledge of this sensitivity is essential for identifying a possible tipping point in the precipitation regime. Existing conceptual approaches24,25 have modelled deforestation in a single box, and are therefore not capable of analysing the cascading impacts of deforestation.

In order to study the cascading, nonlinear effects of deforestation, we construct a nonlinear model of the moisture transport along a trajectory covering the entire Amazon basin. This approach allows for an isolation of the specific relationship between a deforestation-induced decrease of total surface heat flux (including, in particular, the decrease of E), and the positive feedback associated with atmospheric LH release. Furthermore, such a conceptual model is essential to gain a physical understanding of the involved dynamical processes, and to be able to investigate the consequences of successive deforestation for wide ranges of the relevant parameters. We will in the following focus on the monsoon season (December–February) in order to stay in a conservative setting, since impacts of deforestation can be assumed to be more severe during the dry season.

The underlying equations are dictated by the conservation of water in the hydrological cycle:

where A and S denote total moisture content in the atmosphere and soil, respectively, E denotes evapotranspiration, P is precipitation, and R is river runoff. In addition, denotes the divergence of vertically integrated atmospheric moisture flow: at each atmospheric layer λ, this moisture flow is defined as , where Wλ denotes the wind speed. The variables P, E and R will be modelled as effective functions of A and S, respectively (see Figs S1, S2, and S3). Wind speeds W are in our model comprised of a trade wind component and a component representing the amplification of the wind speeds due to the gradient in atmospheric heating between the tropical Atlantic ocean and the Amazon basin (Fig. 1): W = Wtrade + WH. The latter setting introduces the nonlinearity to the model, since WH depends on atmospheric condensation and hence A itself. The model equations are integrated along a sequence of 100 spatial boxes following the climatological trajectory of the low-level winds from the mouth of the Amazon river to the western boundary of the basin (Fig. 1).

Figure 1: Topography of South America, as well as mean 750 hPa Wind fields for the monsoon season (December–February), as obtained from the ERA Interim reanalysis dataset. The Amazon basin is outlined as the blue area. The trajectory along which we integrate our model is indicated by a white contour line, staring at box #1 to the east, and ending at box #100 to the west. The simplification of considering only this one trajectory, which makes our model one-dimensional, can be justified by the fact that the flow is approximately laminar over the Amazon Basin. The source area of the atmospheric moisture inflow over the tropical Atlantic ocean is indicated by a white box. The gradient of atmospheric heating between ocean and land, π = 〈H〉Trajectory − 〈H〉AO, is quantified by averaging over these two spatial regions (see methods section). The map was created using matplotlib’s basemap toolkit37 (http://matplotlib.org/basemap/). Full size image

For the specific formulation of the model, as well as details concerning the employed data sets and simulations, we refer to the methods section below. The results presented in the following will show that the positive feedback associated with atmospheric LH release is indeed the crucial mechanism behind the high moisture inflow from ocean to land, and that there exists a threshold for the extents of deforestation, beyond which this mechanism can no longer be maintained.