Forest recovery prognostics in conservation units of the Atlantic rainforest

Highlights

• A diffusive-logistic model is applied to study forest growth in the Atlantic Rainforest.

• Growth parameters can help gauge the spatiotemporal progress of recovery processes.

• Atlantic rainforest conservation units can reach solid density recovery in 60 years.

Abstract

Forest growth models can provide valuable support tools for forest recovery assessment and forestry management, whether in the form of diagnostic or prognostic. Furthremore, they can be applied to characterize each phytophysiognomy in terms of vegetation growth parameters that and can be applied to gauge the spatiotemporal progress of recovery processes. Up to date, such parameters remain mostly unknown. In this paper, we explore a modelling framework aimed at providing computer-aided prognostics of forest recovery based on the diffusive-logistic growth (DLG) model and present case studies for a number of four preservation areas located in the Brazilian Atlantic rainforest biome. The modelling framework involves the application of vegetation indices derived from satellite images and a computational implementation of the DLG model. The objective of the study is to illustrate how forest restoration and recovery projects could gain from the proposed methodology, due to the fact that the likely outcomes of management practices could be assessed in advance. Additionally, it aims to determine the characteristic parameters of forest growth for a portion of the Atlantic rainforest biome. The diffusion and growth rate parameters from the DLG model were calibrated and they show the evolution of forest density over the years. The results show that the forest recovery process can take several decades to stabilize in the absence of negative interventions in the forest growth. The model and the implementation presented in this work are freely available and they can be an important tool for decision and policy making in what concerns forest recovery.

Introduction

The importance of forests to the maintenance of biodiversity, protection of watersheds, carbon sequestration and mitigation of climate changes is widely acknowledged (Bonan, 2008), bioclimatic equilibrium and maintenance of precipitation levels (Pires and Costa, 2013). In particular, beyond local or regional scales, rainforest systems are argued to sustain large-scale regimes, as it is believed to be the case of the Amazon Rainforest, whose deforestation can trigger a potential tipping point of global climate shift (Boers et al., 2017). While tropical forests are regarded as rather resilient to recurrent disturbances, forest recovery up to pre-disturbance levels can span several decades (Cole et al., 2013), which is far too long comparably to the weather timescale. Furthermore, the onset of new disturbances may prevent forest re-growth to pre-disturbance levels. In Brazil, the remains of the Atlantic Rainforest, which spans from the South to the Northeast of the country, are mostly second-growth forest fragments in early to medium succession stages (Ribeiro et al., 2009). As a result of the urgent demand for large-scale recovery of the Atlantic rainforest, several projects are underway that aim at promoting the restoration of a million hectares of native forests by 2020 and 15 million hectares by 2050 (Global Landscape Forum, 2019).

Given the large time span of current recovery projects and the vast areas covered, the application of mathematical models of forest growth can be of substantial importance to assess forest recovery and provide forest growth prognostics (Acevedo et al., 2012; Richit et al., 2017; Richit et al., 2019). As an example, one can mention the adequate management of environmental processes and risks asapplied to the forest growth and yield (Acevedo et al., 2012; Ashraf et al., 2015; Porté and Bartelink, 2002; Richit et al., 2017). Indeed, mathematical modelling enables the generation of scenarios and prognostics of future development which could hardly be obtained otherwise. Given the importance of forests in the maintenance of biodiversity, water quality, desertification control, flood control, carbon storage, avalanche control, soil fertility, among other forest ecosystem services (Cao et al., 2020; Miura et al., 2015), and the rapid incursion of agriculture and livestock areas into portions of rainforest (Muler et al., 2014), as it occurs in Brazil, it seems that forest growth modelling will increasingly grow in importance and applicability in the coming years.

Different methods have been traditionally applied for forest growth assessment. The methods based on field survey seek to define and apply growth estimators derived from successive assessment of forest biometrics (see Gregoire (1993); Ols et al. (2020)). Forest inventory efforts include the assessment of quantifiable growth indicators such as tree dimensions, form and age. The application of successive studies and calculation of forest growth estimators allow the quantification of forest change in terms of components of growth (such as survivor growth, ingrowth, mortality and cut, as defined and applied by the US Department of Agriculture Forest Service’s Forest Inventory Analysis program - FIA) (Thompson, 2004). The main shortcomings of inventory-based methods are the increased cost, workload, duration and personnel requirements of field surveys, which render them unviable for the evaluation of large forested areas. An alternative and complementary approach is the application of remote sensing products and associated methodologies, such as Leaf Area Index (LAI), for example (Wu et al., 2020). A reasonable advantage of approaches based on remote sensing is they enable the coverage of large areas with high periodicity. Nevertheless, the proper application of remote sensing techniques do require field study for validation (Wu et al., 2020). To provide valuable information about ground-truth, remote sensing indices require field validation such that index values can be adequately interpreted and understood in terms of field reality. A limitation of remote sensing techniques and vegetation indices as applied to the study of forest growth is that variations in vegetation indices alone are unrelated to growth dynamics. In this context, a more insightful approach is to consider such variations as inputs to calibrate mathematical models that can express such variations in terms of growth parameters. A simple reasoning that can help explain this approach is that the same level of index variation in two different stages of forest development will result in different growth parameters because the variation is regarded in terms of its location in the growth curve under consideration (see Acevedo et al. (2012); Richit et al. (2017)).

In this sense, Acevedo et al. (2012) proposed the application of the Diffusive-Logistic Growth (DLG) model as a means of describing natural recovery of forest by means of the interplay between processes of diffusion and reaction. Their work enabled the generation of prognostics of forest recovery for abandoned areas in Puerto Rico for decades ahead, thus anticipating the likely results of natural forest recovery. Later, following the work by Acevedo et al. (2012), Richit et al. (2017) proposed the use of vegetation indices such as the EVI (Enhanced Vegetation Index) to accurately capture vegetation density data from satellite imagery, thus allowing finer calibration and validation of the model equations to real scenes. The authors also presented a high-performance implementation of the DLG model using parallel computing in CUDA platform in which it was possible to provide a 56-fold speedup in the numerical solution of the model as compared to an equivalent sequential implementation. Their work was applied to study forest recovery in riparian buffer strips located in agricultural catchments where the vegetation has an active and important role in the filtering of nitrogen (Richit et al., 2017; Santin et al., 2016). The high-performance implementation, as presented in Richit et al. (2017), allows the study of larger areas with finer grid resolution, since it can handle the solution of linear systems with several million of unknown variables. More recently, Richit et al. (2019) presented an open-source tool that implements the DLG model for applications with GIS. The module r.recovery works with GRASS GIS, an open-source GIS software with a user-friendly interface (Neteler et al., 2012). The r.recovery runs the DLG model equations as proposed by Acevedo et al. (2012) and it incorporates the enhancements contributed by Richit et al. (2017). It provides an easy-to-use simulation facility designed to allow the application of the DLG model by a widespread public of environmental engineers and forest managers that might not be much acquainted with programming. In summary, the evolution of the forest growth modelling framework based on the diffusive-logistic equation has constituted a rather sound approach for studies on forest recovery.

The simplicity of the DLG model and its principles allow the description of forest growth by means of a simple equation with rather intuitive parameters (Richit et al., 2017). An alternative way of taking into account the interaction between different populations of individuals could be taken by using models with competitive terms such as Lotka-Voltera (Acevedo et al., 2012; Jorné, 1977; Lotka, 1910, Lotka, 1956; Takeuchi et al., 2006; Volterra, 1931). The inclusion of equations that represent the populations and their interactions could extend to many species, but beyond the mathematical cost involved in the numerical solution of these numerous coupled equations and the determination of several related parameters, a description of density making distinction among different species would require detailed inventory. Furthermore, obtaining correlations between vegetation indices and plant densities for different species would be quite challenging. Thus, the equation employed by the model guarantees simplicity and applicability given the status and possibilities allowed by the current literature.

Another relevant advantage of the application of forest growth models is the possibility of coupling them to other models, such as climatic, hydrological, forest management and land-use change models (Ager et al., 2020; Komatsu and Kume, 2020; Mayes et al., 2015; Schwaiger et al., 2018). It is a recognized fact that forest growth is sensitive to all those factors, among others; conversely, it is also true that forest conditions influence all of them at different levels and time scales (Allen et al., 2010; Ashraf et al., 2015; Boers et al., 2017; Bonan, 2008; Duffy et al., 2020; Pires and Costa, 2013). Therefore, coupled models can help enhance forest growth prognostics under different scenarios, thus providing deeper understanding of the probable consequences of present actions upon future forest development. In this context, the importance of forest growth prognostics is to provide anticipated assessment to desired economical, social or ecological criteria, whose current evaluation can supply evidences for the need of improved management practices (Richit et al., 2017).

In this paper, we employ the DLG model to study forest recovery in portions of the Atlantic rainforest in Souther region of Brazil. The objective of the study is to illustrate how forest restoration and recovery projects could gain from the proposed methodology, due to the fact that the likely outcomes of management practices could be assessed in advance. Furthermore, it also aims to determine the characteristic parameters of forest growth for a portion of the Atlantic rainforest biome and provide prognostics of forest growth for the decades ahead. Suchprognostics aimed at contributing to the design and review forest management practices and to the understanding of their effects.

This study was carried out by means of the application of r.recovery module, which is an implementation of the DLG model presented in Richit et al. (2017). The results show that the model calibrates well to the forest density data obtained from satellite imagery, and thus it can have the potential to provide rather accurate prognostics of forest recovery for Atlantic rainforest preservation areas. Furthermore, based on previous studies from the literature and the results from our work, we study the hypothesis that the time scale of deforestation and degradation processes is usually much smaller as compared to that of forest recovery processes, which demand from decades to centuries until near completion (Cole et al., 2013). Once validated, it can bring even stronger importance to forest conservation measures. The manuscript is organized as follows: section 2 briefly reviews the model and the r.recovery module and describes the areas under study, the vegetation density maps for each of them. Section 3 presents results and prognostics obtained by means of numerical simulations; section 4 discusses the results and the strengths and limitations of the approach; finally, section 5 gives final remarks and perspectives for future research.