MODELLING FOREST REGENERATION FOR ...

UNIVERSIDADE FEDERAL DA FRONTEIRA SUL -UFFS,

CAMPUS ERECHIM - RS, BRASIL.

LUIZ AUGUSTO RICHIT

MODELLING FOREST REGENERATION FORPERFORMANCE-ORIENTED RIPARIAN BUFFER STRIPS

Erechim-RS,

2017.

Luiz Augusto Richit

Modelling forest regeneration for performance-oriented riparian buffer strips

Trabalho de conclusão de curso apresentado àUniversidade Federal da Fronteira Sul – UFFS– Campus de Erechim, como parte das exigên-cias para obtenção do título de Bacharel emEngenharia Ambiental e Sanitária, sob a orien-tação do Profº Dr. José Mario Vicensi Grzy-bowski e coorientação do Profº Dr. RobertoValmir da Silva.

Professor Orientador: José Mario Vicensi Grzybowski

Erechim-RS,

2017.

Luiz Augusto Richit

Modelling forest regeneration for performance-oriented riparian buffer strips

Trabalho de conclusão de curso apresentado àUniversidade Federal da Fronteira Sul – UFFS– Campus de Erechim, como parte das exigên-cias para obtenção do título de Bacharel emEngenharia Ambiental e Sanitária, sob a orien-tação do Profº Dr. José Mario Vicensi Grzy-bowski e coorientação do Profº Dr. RobertoValmir da Silva.

Aprovado em: 07 de Julho de 2017.

Banca Examinadora:

Professor: Paulo Afonso Hartmann


Membro Convidado: Adriana Dervanoski

Erechim-RS,

2017.

.

O grande rio tem seu trajeto, antes do mar imenso. Copiando-lhe a expressão, a alma percorre igualmente caminhos

variados e etapas diversas, também recebe afluentes de conhecimentos, aqui e ali, avoluma-se em expressão e

purifica-se em qualidade, antes de encontrar o Oceano Eterno da Sabedoria.

‘André L.’

Agradecimentos

Eu agradeço a todas as pessoas que contribuíram de alguma forma à minha jornada, agradeço pois a tudo de bom

que me aconteceste, a tudo de mal que me foi poupado e a todos os percalços que me foram impostos no trajeto.

Agradeço à existência da vida, pela felicidade de ter uma família quando muitos não la têm, agradeço aos subsídios

e ao veículo físico que me foi dado em perfeito estado, agradeço a consciência e o apoio valioso que muitas vezes me

foi estendido.

Obrigado a todos que participaram da jornada laboriosa, àqueles que me ensinaram valores, àqueles que me ensina-

ram conhecimentos, aos meus mestres.

Agradeço em especial aos meus professores que participaram do desenvolvimento desta pesquisa, pela paciência e

pelo auxílio, aos professores Roberto Valmir da Silva e José Mario Vicensi Grzybowski meu muito obrigado e meu

total respeito e consideração. Meu muito obrigado também a minha colega de projeto Charline Bonatto, pelo auxílio e

diversos esclarecimentos e a Tomas Carlotto que pelas suas contribuições abrilhantou ainda mais o trabalho realizado.

A meu irmão, meu pequenino; minha mãezinha amantíssima e ao meu pai querido, muito obrigado! Aos meus demais

familiares que me foram amigos, generosos e exemplo em muitos momentos.

Resumo

As zonas ripárias (ZPs) desempenham um papel importante na conservação dos corpos d’água. No entanto, até o

momento, a crescente degradação da vegetação ripária é uma preocupação importante devido ao risco inerente que

representa para a qualidade e a quantidade de água potável. Por sua vez, a regeneração florestal é conhecida por ser

um processo que evolui em uma escala de tempo de anos, de modo que a regeneração de uma área florestal após

uma perturbação pode demorar várias décadas. Neste contexto, a exploração de modelos de crescimento vegetal pode

contribuir para a compreensão e reconhecimento de diversos aspectos desse fenômeno. Além disso, do ponto de vista

dos projetos de conservação, a aplicação de modelos permite a avaliação de diferentes cenários futuros resultantes da

aplicação de diferentes práticas de gestão, permitindo antecipar os prováveis resultados do processo de gerenciamento.

Neste trabalho, estudamos a aplicação do modelo Logístico-Difusivo de crescimento (modelo LDC) ao problema da

regeneração florestal. Concentramo-nos nas vegetações pertencentes a áreas de preservação permanente, como as ZPs.

A principal contribuição deste estudo é propor e ilustrar uma metodologia minuciosa aplicável como ferramenta au-

xiliar de avaliação e design para projetos de conservação. O estudo é desenvolvido em duas etapas. Baseamo-nos em

resultados recentes que estudam o desempenho das zonas ripárias na remoção de nitrogênio em bacias agrícolas em

que foi aplicado um conjunto de Redes Neurais Artificiais (RNAs) para avaliar a largura das faixas ripárias necessária

para realizar a filtragem de 90% Nitrogênio residual. Tendo isso como base, calibramos e validamos os parâmetros do

modelo logístico-difusivo de crescimento florestal para estimar a evolução da regeneração em zonas ripárias, conside-

rando as larguras obtidas pelas RNAs. Implementamos a solução em GPGPU (General Purpose Graphics Processing

Unit) e, em seguida, simulamos o crescimento para além de quarenta anos para verificar o efeito provável da conser-

vação sobre as zonas ripárias na bacia hidrográfica. Os resultados da calibração e validação mostram que o modelo

logístico-difusivo de crescimento fornece uma descrição temporal e espacial bastante precisa da regeneração florestal.

A aplicação do modelo para o estudo de caso da bacia hidrográfica do rio Ligeiro, no Brasil, mostra que o modelo

pode fornecer informações valiosas para a tomada de decisões no contexto da conservação e gestão ambiental.

Palavras-chave: Zonas Ripárias. Remoção de Nitrogênio. Redes Neurais Artificiais. Modelo Logístico-Difusivo de

Crescimento.

Ecological Engineering 106 (2017) 308–322

Contents lists available at ScienceDirect

Ecological Engineering

jo ur nal home p ag e: www.elsev ier .com/ locate /eco leng

Modelling forest regeneration for performance-oriented riparianbuffer strips

L.A. Richit, C. Bonatto, T. Carlotto, R.V. da Silva, J.M.V. Grzybowski ∗

Federal University of Fronteira Sul, Rodovia RS 135 km 72, CEP 99.700-000 Erechim, RS, Brazil

a r t i c l e i n f o

Article history:Received 6 October 2016Received in revised form 23 May 2017Accepted 29 May 2017

Keywords:Riparian buffer stripNitrogen removalArtificial neural network ensemblesDiffusive-logistic growth

a b s t r a c t

Riparian buffer strips (RBS) play an important role in the conservation of water bodies. Yet to datethe increasing degradation of riparian vegetation is a major concern due to the inherent risk it posesto quality and quantity of drinkable water. In turn, forest regeneration is known to be a process thatevolves in a time-scale of years, such that the regeneration of a forested area after a perturbation cantake several decades. In this context, the exploration of models of vegetation growth can contribute to theunderstanding and acknowledgement of diverse aspects of such phenoma. Further, from the standpointof conservation projects, the application of models allows the assessment of different future scenariosresulting from the application of different management practices, thus allowing anticipating the likelyoutcomes of the management process. In this paper, we study the application of the diffusive-logisticmodel (DLG model) to the problem of forest regeneration. We concentrate in vegetation belonging to per-manent preservation areas, such as RBS. The main contribution of this study is to propose and illustratea thorough methodology applicable as auxiliary assessment and design tool for conservation projects.The study is developed in two steps. We build upon recent results that study on the performance ofriparian buffer strips in the removal of nitrogen in agricultural catchments in which an Artificial NeuralNetwork Ensemble (ANNE) was applied to evaluate the riparian buffer strip width needed to accom-plish filtering of 90% of the residual nitrogen. On this basis, we calibrate and validate the parameters ofthe diffusive-logistic model of forest growth to estimate the evolution of regeneration in riparian bufferstrips, considering the buffer widths obtained by the ANNE. We implement the solution in GPGPU (Gen-eral Purpose Graphics Processing Unit) and then simulate for forty years ahead to verify the likely effectof conservation upon the riparian buffer strips in the watershed. The results of calibration and valida-tion show that the diffusive-logistic model provides a rather accurate temporal and spatial account offorest regeneration. The application of the model to a case study of the Ligeiro River watershed, Brazil,shows that the model can provide valuable insights for decision-making in the context of environmentalconservation and management.

© 2017 Elsevier B.V. All rights reserved.

1. Introduction

Numerous scientific studies worldwide have discussed theimportance of the riparian buffer strips (RBS) in the conserva-tion of species and habitats, water courses, water quality andquantity (Phillips, 1989; Mander et al., 1997, 2005; EnvironmentalProtection and, 2005; Correll, 2005; Syversen, 2005; Sahu and Gu,2009; Zahawi et al., 2015; Santin et al., 2016). Among the well-established facts in this regard, it is known that RBSs accomplisha number of essential conservation functions, such as filtering of

∗ Corresponding author.E-mail addresses: [email protected] (R.V. da Silva),

[email protected] (J.M.V. Grzybowski).

surface and subsurface flow, mitigation of erosion in water bodies,improving microclimate, trapping suspending sediments, adher-ing and assimilating nutrients, binding dissolved pesticides, amongothers (Mander et al., 1997; Correll, 2005). The contamination ofwater by residues of nutrients from agriculture croplands is ofspecial concern. This is due to the fact that nutrient inputs occur sys-tematically along the years, thus having cumulative effects. Indeed,nutrient contamination is one of the main reasons for which theregeneration and maintenance of RBS has become a central argu-ment in favor of water quality. The importance of vegetation residesin the plant uptake and storage of nitrogen, which reduces nitro-gen concentration in the discharge flow. As such, the RBS acts likea filter. Nevertheless, this requires that buffer strips have sufficientwidth and vegetation density, such that they can handle the nutri-

http://dx.doi.org/10.1016/j.ecoleng.2017.05.0440925-8574/© 2017 Elsevier B.V. All rights reserved.

L.A. Richit et al. / Ecological Engineering 106 (2017) 308–322 309

ent load to which they are subjected. While denitrification appearsas the only form of permanent nitrogen removal (Boz and Gumiero,2016; Pinay et al., 1993; Gundersen, 1991), the presence of RBSplays an important role in the process. During the denitrificationprocess, oxidized forms of nitrogen such as nitrates and nitrites arecontinuously reduced through chemical reactions promoted by themetabolism of specific bacteria to the N2 molecular nitrogen condi-tion that corresponds to the permanent removal of organic nitrogen(Bothe et al., 2006; Dendooven and Anderson, 1994; Pinay et al.,1993). As the process must occur under adequate moisture condi-tions and sufficient amounts of organic carbon, the maintenance ofRBS are acknowledged to be favorable for reactions to occur sat-isfactorily (Pinay et al., 2000). These conditions are provided byRBS as plant cover allows greater moisture retention and nutri-ent cycling by continuous degradation of organic material, whileit also provides organic carbon required (Boz and Gumiero, 2016;Groffman et al., 1991; Philip Robertson and Biber, 1988). The fac-tors that influence degradation have been reported in a variety ofresearches, such as soil redox potential conditions, temperature,groundwater level, soil permeability, moisture content, succes-sional level and soil cover (Boz and Gumiero, 2016; Groffman et al.,1991; Hill et al., 2000; Lowrance, 1992; Newcomer et al., 2012).Thereby, the maintenance of green areas, especially RBS, as rec-ognized to be fundamental from ecological point of view. In thissense, restoring and preserving RBS areas has a special potential forwater quality control through the removal of contaminants suchas nitrogen through the improvement of denitrification process-ing conditions (Boz and Gumiero, 2016; Lowrance, 1995). Althoughthe functions and importance of RBS are widely acknowledged, thedegradation of forested areas in the vicinity of water bodies is arecurrent problem worldwide (Phillips, 1989; Mander et al., 1997,2005; Parkyn, 2004; Environmental Protection and, 2005; Sahu andGu, 2009; Kuglerova et al., 2014). Thereby, a major source of con-cern is the long time it takes to reverse a degradation process. Whilethe degradation of large areas of forest can be a matter of monthsor a few years, a regeneration process requires several years to set-tle and at least a couple decades to estabilize, to depend on thebioma (Cole et al., 2014). This poses a tremendous challenge todecision-makers on the planning and management practices to beapplied in each case. In this context, the application of mathemat-ical models can be of help as they allow management practicesto be put to test before they are actually applied in the field. Fur-ther, model projections can lead to a rather clear idea on whatthe observed status of the regeneration process should look likeat any given time. This allows managers to evaluate the real pro-cess against the observed one and test mid-course managementpractices at any point of the process. A number of studies haveaddressed forest recovery by means of diverse methodologies. Acomprehensive survey on forest recovery with emphasis on thestatistical analysis of post-disturbance recovery time across differ-ent biomes is presented in Cole et al. (2014). Among the interestconclusions, it is found that recovery times vary considerably withthe geographical location, e.g., forests in Central America and Africawere found to generally recover faster than those in South Amer-ica and Asia (Cole et al., 2014). As another important research tool,one can cite the Forest Vegetation Simulator (FVS), a decision sup-port tool developed by USDA Forest Service and in use for over 30years Crookston and Dixon (2005). The FVS encompasses models offorest dynamics that simulate forest vegetation response to man-agement actions, natural succession and disturbances (Crookstonet al., 2010; USDA and U.S., 2010). A recent study of modeling forestgrowth was presented in Acevedo et al. (2012) by means of the DLGmodel. Unlike the FVS, which implements detailed modeling to thetree level, thus requiring detailed inventory of forest and individualtrees attributes, the DLG model works solely on the basis of vege-tation density over the forested domain of interest. In the case of

Acevedo et al. (2012), the DLG model is applied to the evaluationof forest recovery in Puerto Rico for an interval of 40 years. Besidespresenting results of practical interest, the authors point the impor-tance of the DLG model not only in the study of forest recovery, butalso to the study of changes in the rate of change and the rate ofspread of vegetation over time for a particular location of forestedarea. This reinforces the importance of adequate model calibrationto the local conditions of the region of interest. As an instance, theFVS is reported to have twenty-two variants aimed at accountingfor variations in local specificities of forested areas of the UnitedStates, British Columbia and Canada (Crookston and Dixon, 2005).Another instance of modeling tool applied to decision support sys-tem is NED (Forest Ecosystem Decision Support Software) (Tweryet al., 2000, 2005). Also developed by the USDA Forest Service,NED is a project-level planning assistance tool with flexible designand intensive requirement for inventory data (Twery et al., 2000,2005). Further examples may be found in the literature. In general,forest growth models available in the literature regard individualgrowth assessment. For example, the AmapSim software presentedin (Barczi et al., 2008) is based on botanical principles and is ableto simulate the evolution of individual growth in 3D on the basisof data derived from real plants, taking into account ramifications,bud formation, leaf production, differentiation and formation of lat-eral shoots and axial growth, among others. The author presents acomplete model for growth simulation with support for differentspecies from the knowledge of detailed botanical characteristicsand even reports its use to predict fossil species (Barczi et al.,2008). Other models also follow a similar feature as they focuson individual growth. The work of Twilley et al. (1999) presents anumerical model for simulation of vegetation growth in mangroveareas, by means of the so-called FORMAN model. In such model,the conditions of salinity, temperature, nutrient availability andluminosity are considered and growth is described by increasingthe diameter-at-the-chest of the individuals. It is worth remarkingthat the application of this model requires a very detailed inven-tory of the area to be simulated, since the initial conditions forgrowth simulation need to be properly assigned for each individual(Twilley et al., 1999). Some models, such as the Capsis model DeColigny et al. (2003), de and Nicolson (2006), StoMat (Stochasticmatrix models) (Gourlet-Fleury et al., 2004) and SELVA (Gourlet-Fleury., 1999; Gourlet-Fleury et al., 2005) incorporate models ofindividual growth, the relation of seed dispersal and growth asa function of distance from the source and even the competitionamong individuals, as in the SILVA simulator (Pretzsch and Biber,2002). In turn, Porté and Bartelink (2002) present an extensivestudy on forest growth models, raising concern about the limi-tations of the single-tree growth models commonly adopted. Aparticularly important point is that the study of large areas bymeans of single-tree models may consume too much time andeffort, since they require detailed tree inventory. In this context,the DLG model Acevedo et al. (2012), appears as an alternativeto single-tree models, since it regards forested areas as a wholewhile it is tailored to describe the time evolution of forest den-sity as a function of diffusion and growth rate parameters (Acevedoet al., 2012). Bottom line, computer models and tools can effectivelypromote the knowledge-based decision making in the context offorest management and policy making, thus contributing to ecolog-ical, economic and social well-being. Regarding forest managementpractices and their influence upon ecosystem services (ES), recentstudies propose the application of models to simulate and optimizeobjective functions related to desired ES capabilities (Diaz-Balteiroand Romero, 2003; Bagdon et al., 2016). Indeed, the use of modelingand programming techniques is reported to allow the identificationof feasible solutions to plan for management goals (Bagdon et al.,2016). In the same direction, the application of artificial intelligencetechniques has contributed to the assessment of feasible solutions

310 L.A. Richit et al. / Ecological Engineering 106 (2017) 308–322

to environmental problems in a wide range of situations (Gardnerand Dorling, 1998; Maier and Dandy, 2001; Daliakopoulos et al.,2005; Lallahem et al., 2005; Garcia and Shigidi, 2006; Sahoo et al.,2006; Tosh and Ruxton, 2007; He et al., 2011; Yoon et al., 2011;Santin et al., 2016). The increasingly large availability of environ-mental data makes neural networks particularly interesting dueto their intrinsic ability to learn from them. Of particular interestin this study, the design of performance-oriented RBS was shownto be feasible as approached from the viewpoint of an ArtificialNeural Network Ensemble (ANNE) (Santin et al., 2016). As a result,the ANNE was capable of learning from a dataset how to approxi-mate the width of the RBS capable of filtering 90% of the nitrogenintake from uphill agriculture as a function of vegetation cover type(VCT), soil type (ST), mean nitrogen intake (MNI) and removal effi-ciency (RE) (Santin et al., 2016). In this paper, we combine differenttechniques proposed in the literature (ANNE, DLG) and propose acomprehensive methodology to the study of forest growth fromthe viewpoint of management and engineering. Towards this, wecombine the application of an ANNE to the design of RBS widthoriented to performance (as originally proposed in Santin et al.(2016)) to the application of the DLG model of forest growth, as pro-posed in Acevedo et al. (2012). The main contribution of the paperis to propose a comprehensive and practical approach that allowsthe design of performance-oriented RBS. Following the proposedframework, not only the attributes of the RBS are assessed, butalso design requirements can be introduced and a detailed accountof its time evolution can be obtained. To illustrate the proposedapproach, we apply it in the study of regeneration of RBS in theLigeiro River watershed, Brazil. The DLG model is calibrated andvalidated using Landsat images and then applied to simulate veg-etation growth up to 30 years ahead. We show that the proposedapproach is highly reproducible and, upon further development,can be made an effective design tool.

2. Materials and methods

This section addresses the DLG model (Acevedo et al., 2012) andits discretization, the procedures for image acquisition and pro-cessing and also the procedures for training, validation, test andcomposition of the ANNE. A flowchart of the methodological pro-cedures is presented in Fig. 1.

2.1. A model of forest recovery

To describe forest recovery, we consider the diffusive logisticgrowth model, as presented in Acevedo et al. (2012). The modeldescribes forest recovery as a combined process of diffusion andlogistic growth. Diffusion is the net flow of particles down a concen-tration gradient, as described by Fick’s law. In the two-dimensionalform, for a concentration u, the Fick’s lack can be stated as

J = −D∇ · u (2.1)

where J is the amount of substance per unit area per unit time, Dis the diffusion coefficient and x, y are the position coordinates,all relative to the concentration u(t, x, y) (Holzbecher, 2007). Inthis formulation, we are assuming that the diffusion coefficientD is homogeneous along the spatial domain and constant overtime. This means that the diffusion flux in a position x is pro-portional to the negative of the gradient of concentration in thatposition (Gordon Skellam, 1951; Edelstein-Keshet, 1988; Okuboand Levin, 2013). In turn, the logistic growth model describes pop-ulation growth subjected to a limitation in the supply of resources,originally proposed by Verhulst (1845, 1847) and subsequentiallyapplied in the study of several forms of population growth prob-lems, both theoretical and practical (Melica, 2014; Nasell, 2001;Peleg et al., 2007; Rosen, 1984). The logistic model states that the

rate of change of a population of size U subjected to a constantgrowth rate r in an environment with carrying capacity K can bemodelled as (Fig. 2)

∂u∂t

= ru(

1 − u

K

)(2.2)

The solution of the logistic model in Eq. (2.2) can be found ana-lytically and it is given by

u(t) = Ku0ert

K + u0 (ert − 1)(2.3)

and from Eq. (2.3) we note that, for any initial condition on thepopulation size or density, the population converges to the carryingcapacity as time tends to large values. This can be expressed moreformally as

limu(t) = Kt→+∞

(2.4)

which indicates that u(t) = K as t → +∞. Without loss of generality,we consider U(t, x, y) as a density variable whose values lie in theinterval [0, 1].

Consider the continuity equation in two dimensions for thequantity u, given as

∂u∂t

= −∇ · J + q (2.5)

where q = q(t, x, y) is a source or sink term. Substituting Eqs. (2.1 and2.2) in Eq. (2.5) and considering q(t, x, y) to behave as the logisticequation for K = 1, one comes to

∂u∂t

= Du

(∂2u

∂x2+ ∂

2u

∂y2

)+ ruu (1 − u) (2.6)

Eq. (2.6) is named the Diffusive Logistic model (Holmes et al.,1994; Okubo and Levin, 2013; Acevedo et al., 2012). We followAcevedo et al. (2012) and apply the Crank-Nicolson scheme ofFinite Differences Crank and Nicolson (1996) to evaluate the modelnumerically. The boundaries of the RBS region are assumed to beNeuman, with ∂u = 0, that is, a no-flux condition.

2.2. Discretization and solution of the DLG model

We follow the procedure in Acevedo et al. (2012) and dis-cretize the DLG model using the Crank-Nicolson scheme (Crank andNicolson, 1996). The time derivative in Eq. (2.6) is approximatedwith first-order forward difference, that is,

∂u∂t

≈ u (x, y, t + �t) − u (x, y, t)�t

(2.7)

where �t is the time step. The spatial derivatives are approximatedwith second-order differences

∂2u

∂x2≈ u (x + �x, y, t) − 2u (x, y, t) + u (x − �x, y, t)

(�x)2(2.8)

∂2u

∂y2≈ u (x, y + �y, t) − 2u (x, y, t) + u (x, y − �y, t)

(�y)2(2.9)

We assume the parameters Du and ru are constant over time andspace and the carrying capacity is Ku = 1. Taking the finite differ-ence approximations from Eqs. (2.7), (2.8) and (2.9) to Eq. (2.6) andexpressing the value of the continuous function u(x, y, t) in a point(xi, yj) of the grid at time step tk as Uk

ij, one obtains an expression

for the finite-difference approximation of Eq. (2.6). After some alge-


Fig. 1. Flowchart of the methodological procedures.

braic manipulations and assuming �x = �y, and defining � = �tDu�x2 ,

it can be written as

(1 + 4�)Uk+1i,j

− �(Uk+1i+1,,j + Uk+1

i−1,,j + Uk+1i,,j+1 + Uk+1

i,,j−1

)=

· · · =(

1 − 4� + ru

(1 − Uk

i,j

))Uki,j

+�(Uki+1,,j + Uk

i−1,,j + Uki,,j+1 + Uk

i,,j−1

)(2.10)

By rewriting Eq. (2.10) in compact format as a matrix equation,it reads

AUk+1 = BkUk (2.11)

The solution Uk for the time step k is known and this makes BUk

known. We define bk = BUk to express the linear system in theusual notation AUk+1 = bk. The formulation of the problem guaran-tees that, for each time step k, the linear system in Eq. (2.11) has aunique solution vector Uk+1, which can be expressed as

Uk+1 = A−1bk (2.12)

Now, A is a constant sparse and symmetric matrix, and as the systemhas to be solved once at every time step (not included the initialcondition U0).

We solved the resulting linear system in Eq. (2.11) using theStabilized Bi-Conjugate method with error tolerance � = 10−9 foreach time step. The solution was implemented and computed inGPGPU (General Purpose Graphics Processing Unit) using CUDA(Computer Unified Device Architecture) parallel programming andcomputing platform (NVIDIA, 2007; Nickolls and Buck, 2008) andthe CUSP library Bell and Garland (2013). To this end, we employedan NVIDIA(TM) GeForce(TM) GTX 1060 graphics card device alongwith an Intel(R) Core (TM) i7 − 7700 host processor.

2.3. Image acquisition and processing

The Landsat 5 and 8 scenes were acquired from the US Geologi-cal Survey (US Geological Survey, 2000, 2010, 2016) and convertedfrom Digital Number (DN) to reflectance in the software GRASS GIS7.0 using the module [i.landsat.toar] (Development Team, GRASS,2014). The scenes from the Landsat 5 TM are from the years 2000and 2010, path/row=222/79, DOY = 38 and 49, respectively. Thescene for the year 2016 is from the OLI/TIRS sensor, path/row =222/79 and DOY=18. The resulting image was converted to veg-etation density by means of the implementation of EnhancedVegetation Index (EVI) in module [i.vi] (Development Team, GRASS,2014), and then saved as a matrix of numeric entries corresponding


Fig. 2. Illustration of logistic growth (above) and diffusive-logistic growth (below).

to the vegetation density in each pixel of the image. This procedurewas performed for each of the three scenes to serve as initial/finalconditions for calibration/validation of the model and as initial con-dition for application in the assessment of RBS regeneration in theLigeiro River watershed.

2.4. Calculation of vegetation density

The vegetation density for the calibration, validation and appli-cation of the model was calculated by means of the EnhancedVegetation Index (EVI) (Solano et al., 2010). One principle behindthe EVI is the estimation of atmospheric effects by means of thedifference between red and blue band reflectances, which scaleswith the concentration of aerosols (Solano et al., 2010). Anotherprinciple is the reduction of distortions of light reflected by groundcover below the vegetation, which influence the reflectances inthe red and near infra-red bands (Solano et al., 2010). Thus, theEVI seeks the optimization of vegetation signal by intensifying theresponse in regions with concentration of biomass. The equationfor vegetation density in an image pixel is given by

EVI = GNIR − RED

NIR + C1 · RED − C2 · BLUE + L(2.13)

where G is a gain scaling factor, C1 and C2 are aerosol resistancecoefficients, L is the canopy adjustment parameter and NIR, RED,BLUE are reflectance in the near-infrared, red and blue spectralbands, respectively. In this paper, the EVI in Eq. (2.13) is appliedto Landsat images in order to obtain the initial conditions to thecalibration, validation and application of the model. We applythe standard parameter values G = 2.5, C1 = 6, C2 = 7.5 and L = 1(Solano et al., 2010). The initial and final conditions for calibra-tion/validation of the model were obtained from Landsat scenes,respectively in US Geological Survey (2000, 2010).

2.5. Calibration and validation of the DLG model

The calibration of the model is aimed at identifying the cou-ple of parameters Du, ru that minimize the Root Mean SquaredError (RMSE). To this end, a systematic search was performed overthe parameter space Du × ru, starting from coarser grid resolutionsand successively increasing the resolution around points of minimafrom coarser levels. The calibration and validation were performedconsidering an area of permanent conservation with the same typeand pattern of vegetation as the region of interest. In the calibrationprocess, we used the half of the image of vegetation density, whilethe other half was saved for validation. The validation process wasalso performed using the RMSE.

2.6. Artificial Neural Network Ensemble (ANNE) and theestimation of RBS width for the filtering of nitrogen

The application of an ANNE to the estimation of RBS width wasproposed in Santin et al. (2016). We present a summary of the keypoints that are relevant to the methodology proposed in this paper.

2.6.1. The training, validation and test dataThe training, validation and test of the neural networks

were performed with data originally published in a number ofindependent studies which were collected and reproduced inEnvironmental Protection and (2005). The data include mean nitro-gen influent (MNI, in ppm), mean nitrogen effluent (MNE, in ppm),removal effectiveness (RE, in %), vegetative cover type (VCT, clas-sified into grass, grass forest or forest), soil type (ST, classified intosand, silt, clay and combinations) and buffer width (BW, in meters).These indicators are associated to the mitigation potential of non-point source nutrient pollution. In turn, nutrient pollution is mainlyassociated to the accumulation due to the loss of nitrates from ups-lope agriculture areas. The dataset from Environmental Protectionand (2005) provided 39 complete records from which the amountsof nitrate and total N loads was associated with the indicators MNI,


RE, VCT and ST. Such indicators were used as inputs to the neuralnetwork while BW was used as output. The sigmoid function waschosen as activation function of the neuron. To scale the data toregion of interest of the sigmoid function under this application,the data were linearly mapped to the interval [0, 1]. Thus, the num-ber of inputs to each ANN in the ensemble is NI = 4 and the numberof output is NO = 1. The input variable ST was converted to theircharacteristic hydraulic conductivity coefficients as found in theliterature Gonc alves and Libardi (2013). In turn, vegetation typeswere converted to density parameters in the interval [0, 1].

2.6.2. The application dataThe geomorphological information of the study area was

obtained from the digital elevation model (DEM) (Valeriano, 2002,2004). The DEM was processed using the open source softwareGRASS GIS 7.0 (GRASS, 2014). The raster maps were derivedby means of the module [r.watershed] and then the watershedslopes, drainage directions, sub-basins and stream segments wereobtained. A minimum sub-basin area threshold was chosen to sub-divide the watershed such that every sub-basin contributes for atleast one stretch of river. The stream segments were delineated bymeans of a calibrated channel initialization threshold which defineswhere a river begins (Montgomery and Dietrich, 1989, 1992). Thedelineated streams were compared to the location of river headsidentified by satellite images in order to check the results. The VCTfor the region of interest was obtained by means of image process-ing and in loco validation of a dozen key points. The scene (Landsat8 scene in US Geological Survey (2016)) was obtained from theUS Geological Survey (US Geological Survey, 2014). The land useclassification was performed using the unsupervised cluster anal-ysis algorithm for pixel grouping of the watershed land use in 20classes. Such classes were grouped into 3 classes of vegetation covertype based on vegetation density. Each class was assigned an indexaccording to vegetation index, resulting in classes 0.7 (forest), 0.5(grass forest) and 0.3 (grass). Next, the MNI for each sub-basin wasestimated by means of experimental data from soybean croplandsin the literature (Harmel et al., 2006). The MNI was obtained underthe hypothesis that the contribution of each sub-basin scales withits cropland area and concentrates equally along the length of thestretch of river to which it contributes for a constant depth. A 20-year time series with daily rainfall data were obtained from eightrainfall gauges, while river level was obtained from one river levelgauge from the National Agency of Water Resources (ANA) web-site (ANA, 2015). The Inverse Distance Squared Weighting (IDW)algorithm was applied to interpolate the rainfall data within thewatershed. The amount of evapotranspiration was estimated by

means of water balance calculation for the period. As a result,the average annual rainfall, evapotranspiration and runoff wereobtained as 2210.6 mm, 1247.5 mm and 963.1 mm, respectively.As the major interest resides in the sub-superficial transport thattakes places in the hillslopes, we regard the amount of precipitationthat generates runoff. As a result, the estimated MNI for the j − thsub-basin was estimated as

MNIj = 1�Nbasisj ·

Acroplandj

Lriverj

· 1

Prunoffj

(2.14)

where MNIj (ppm) is the mean nitrogen influent for the j − th sub-basin, C (mg m−2) is the typical nitrogen load for the respectivecropland, � is the soil porosity, Lriver

j(m2) is the area of the longi-

tudinal section of the river that receives contribution of the j − thsub-basin, Acropland

j(m2) is the area of the j − th cropland, Prunoff

j

(l m−2) is runoff. Considering the river morphology, it is assumedthat all longitudinal sections of the river have unitary depth.

2.6.3. Architecture, training and validationThe choice of the network architectures was based on the upper

and lower limit equations for the number of neurons in the hiddenlayer (Netch-Nielsen, 1987). According to Netch-Nielsen (1987), thenumber of hidden layer neurons that ensures that the neural net-work is able to approximate any continuous function is given byNH ≤ 2NI + 1, where NH is the number of neurons in the hidden layerand NI is the number of inputs. Further, it is known from the workin Netch-Nielsen (1987) that the number of neurons in the hiddenlayer must observe the upper limit NH ≤ NR

NI+1 , where NR is the num-ber of records in the dataset. From the dataset, NI = 4, NR = 39 andthen we consider architectures featuring NH in the range 2 ≤ NH ≤ 7in order to satisfy both restrictions. Thus, the network architec-tures considered were 4-2-1 to 4-7-1. We refer to Figs. 3-(a) foran example of a 4-5-1 architecture). Figl 3-(b) shows the processof obtaining the ANNE output from the outputs of the individualANNs. The neuron activation function was chosen to be the logisticfunction (Haykin, 1999).

2.6.4. Test and selectionThe test of the individual ANNs was performed by evaluating

their response to unseen inputs from the test set. The individualnetworks with smallest output error levels were selected to com-pose the ANNE. The number of ANNs to compose the ensemblewas established such that the largest error would not overcome20%. Further, an ANN with small error would be admitted into theANNE if and only if its error is uncorrelated or loosely correlated to

Fig. 3. (a) Example of ANN architecture featuring an Input-Hidden-Output relation 4-5-1 (four input variables, five hidden nodes and one output variable). (b) Relationbetween the individual ANN output and the ANNE output. Extracted from Santin et al. (2016).


the errors of previously chosen members of the ensemble. Towardsthat, the Pearson correlation coefficient was applied to evaluate thecorrelation in output error across different individual ANNs. Fol-lowing these criteria, 10 individual ANNs were selected to be partof the ANNE.

2.6.5. Application of the ANNEThe ANNE was applied to design a RBS to the Ligeiro River water-

shed on the basis of the input parameters of each sub-basin of thewatershed. The input parameter RE was set to 90% and this can beregarded as a design criterion. It could be that the RE is set to dif-ferent values according to the filtering effectiveness required for aparticular stretch of river, i.e., nearby a water catchment location,for example. Vegetation density in the watershed was evaluatedby means of land use classification in software GRASS GIS 7.0. Thesoil hydraulic conductivity was taken as 14.6 cm day−1, a typicalvalue for the Brown latosol in the region according to Gonc alvesand Libardi (2013).

For further details on calibration results, test results and sensi-tivity analysis of the ANNE, we refer to Santin et al. (2016).

2.7. Application of the model

The model is applied to the RBS belonging to the Ligeiro Riverwatershed. Since the picture element size of the Landsat image is30 m × 30 m, we round up the results of the application of the ANNEto the next integer that is multiple of 30 meters, and this will beconsidered to be the buffer width. To obtain the integration domain,we apply a buffer around the river courses pointed by the digitalterrain model (DTM) in GRASS GIS 7.0. The model is simulated to 10,20, 30 and 40 years ahead from the initial conditions U0 obtainedby means of application of EVI to the Landsat scene in US GeologicalSurvey (2016).

2.8. Strengths and limitations of the framework

2.8.1. Artificial neural network ensembles’ responses to thefeatures and requisites of riparian buffer strips

It is widely recognized that artificial neural networks can givevery accurate responses when adequately trained, validated andtested (Chellapila and Fogel, 1999; Daliakopoulos et al., 2005;Dietzel et al., 2012; Garcia and Shigidi, 2006; Gardner and Dorling,1998; Gopinath and Reddy, 2000; He et al., 2011; Lisboa and Taktak,2006). To this end, the data fed to the network must be as repre-sentative as possible of the phenomenon to be black-box modeled.As such, the approach presented in this paper, as based on ANNEs,inherits these qualities and premises. In the presence of enoughdata and adequate training, validation and testing, the RBS featuresas provided by the ANNEs can give a trustworthy approximation,especially to problems where conceptual models cannot be easilyapplied (Santin et al., 2016).

2.8.2. The application of Enhanced Vegetation Index (EVI) inLandsat satellite images

The application of EVI to assess vegetation density comes as analternative to the land-use classification, as proposed in Acevedoet al. (2012). The advantages of the application of EVI (or any othervegetation index) are that (i) it results in a pixel-by-pixel vegetationdensity and (ii) it can be readily scaled to the range of the forestdensity variable u(t, x, y) in the diffusive-logistic model. Further,vegetation indices are better indicators of lushness and health ofthe vegetative cover as pictured by Landsat images.

2.8.3. GPGPU implementation of the diffusive-logistic modelThe solution of the DLG model was referred to as computation-

ally demanding in Acevedo et al. (2012), due to the large number

of points of the resulting mesh (presumably about 4 million). Inorder to tackle this issue, the authors redefined the original gridcells (30 m × 30 m) calculating the percent cover of each land coverclass to generate 1-km grid cells, thus obtaining a mesh of 33 × 139grid cells. In order to keep the original resolution of 30 m × 30 m,which can provide a better solution for the model, we workaroundthe high computational demand by implementing a GPGPU solu-tion to the problem using CUDA/C. Through this implementation,we perceived an approximate 50-fold reduction in computationaltime relatively to the serial CPU implementation.

2.8.4. Solution of the irregular mesh defined in a watershedThe spatial pattern occupied by a river in a watershed is known

to be highly irregular, being frequently referred to have frac-tal structures (Tarboton, 1996; Campos and Fort, 2006). Underthese conditions, the definition of boundaries conditions for diffu-sion problems becomes a logistically complex task, as observed inAcevedo et al. (2012). To bypass this difficulty, we apply the ANNEsolution of RBS width and the Digital Elevation Map of the water-shed as inputs and automatize the generation of the correspondinglinear system by means of a computer routine. The routine wasdesigned to read the mesh points from the input matrices to definethe RBS of interest for every stretch of river and then to apply theno-flux boundary condition all over the mesh. As a result of theautomation of the task, we hope that the methodology proposed inthis paper can find more widespread applicability.

3. Case study: simulation of forest regeneration in theLigeiro river watershed, Brazil

3.1. Characterization of the watershed

The Ligeiro River watershed is situated in the city of Erechim,Rio Grande do Sul state, Brazil, between 27◦39′ S and 27◦43′ S, and52◦14′ W and 52◦18′ W. It is 21.18 km2 in area and its elevationsabove the sea level range from 661 m to 815 m, approximately. Theterrain slopes vary between 0.02 and 0.22. Soils throughout thewatershed are classified as Brown latosol based on the color of Bhorizon (EMBRAPA and IBGE, 2011). The Ligeiro River watershed islocated in a region of Atlantic Rainforest, a bioma in which the veg-etation is composed primarily of mixed ombrophile forest (Rambo,1956; Souza, 2007), although its current situation has sufferedsevere influence of anthropic activities, from which we highlightagriculture (Geist and Lambin, 2002). For natural conditions of for-est region, the vegetation is characterized by the presence of largetrees with species that form canopies of deciduous, semi decid-uous and evergreen trees during the winter (Hueck, 1953; Klein,1972). The typical condition of forest is the perennial trees, a frac-tion of which lose all or part of leaves in the cold seasons. Thetrees stand out for having long life, reaching live centuries. Theseforests are most known for harboring the Araucaria angustifolia –the Brazilian pine species which is subject to intensive research,which raises concerns about its conservation (Bittencourt et al.,2004; Bittencourt and Sebben, 2007; Stefenon et al., 2007) as wellas being responsible for the conspicuous characteristic of the plantformation to which it belongs (Klein, 1972; Backes and Irgang,2002), is income and food source for local people and wildlife ingeneral. Land use analysis has shown that 4.94 km2 of the water-shed area are identified as forests and 16.04 km2 as crop lands.According to the Brazil’s Forest Code, the watershed should be2.10 km2 in area of riparian vegetation (taking into account thirtymeters along the river length and fifty meters around every headriver). However, it is only 0.94 km2. Moreover, the watershed hasbeen subjected to drought events, which compromised the watersupply and raised concerns from water resource managers and soci-


Fig. 4. Location of the Ligeiro River watershed in Erechim, Brazil, and elevation map showing the drainage network and the water supply reservoir. Elevations in the watershedrange from 661 to 815 m. Extracted from Santin et al. (2016).

Fig. 5. Map of land use in the Ligeiro River watershed: (1) cropland, (2)intermediate-density vegetation – grass-forest and (3) dense vegetation – forest.Extracted from Ref. Santin et al. (2016).

ety as well. The elevation map of the watershed and the map of landuse are shown in Figs. 4 and 5, respectively. The current situationof the riparian vegetation in the watershed is shown in Fig. 5. Thesesoils constitute the largest class of territorial expression and agri-cultural potential of the country, being explored with various crops,reforestation and pasture (Ker, 1998).

3.2. ANNE and the design of performance-oriented buffer zones:the case of nitrogen filtering

We base our study in the results presented in Santin et al. (2016),where an ANNE was trained, validated and tested to design a RBS tothe Ligeiro River watershed. The main design requirement is that

the RBS should be capable of filtering at least 90% of the MNI. Thereason why we set RE to 90% was the characteristic nitrogen loadof agricultural catchments for the watershed in which the studytook place. Moreover, the RE value might be set up in order tocomply with environmental standards for residual nitrogen limitsin the river at the target basin. Diffuse sources of pollution rep-resent a significant fraction of the pollution of watercourses, andunlike point sources that can be well defined and measured, theseare generally estimated (Birgand et al., 2007). Each country has,according to its control mechanisms and desired quality, standardconcentration values of the contaminants it considers. A simpleway to define removal efficiency is to base it on standard valuesaccording to legislation. In the case of the basin under study, byBrazilian laws, maximum concentration values are defined accord-ing to the classification of the water body (CONAMA BRASIL, 2005).But these legal standards are not always based on the natural abil-ity of self-purification and assimilation as they may be set to valuesthat are not actually attainable. A study that gathers an analysis onthe assimilation and removal capacity of nitrogen and phosphorusfrom diffuse sources in riparian zones in different types of basins bymeans of the analysis of numerous published works, reveals thatthe maximum efficiency varies according to the vegetative cover-age, succession stage, type of land use (Mander et al., 1997). In thisway, it seems more adequate to define maximum efficiency accord-ing to the intrinsic capacity of the type of plant formation. Nitrogenremoval efficiency values for forest riparian zones range from 82to 87% (Peterjohn and Correll, 1984; Schwer and Clausen, 1989;Mander, 1985) in older forest areas up to 95% or more in young andgrowing forests (Mander, 1985; Schwer and Clausen, 1989; Mitschet al., 1979; Knauer and Gilliam, 1989; Jacobs and Gilliam, 1985).Thereby, a sensible value for RE according to literature review isabout 90% as verified in Mitsch et al. (1979). As a result, the ade-quate RBS width for every stretch of river in the watershed wascalculated. The basin was subdivided into 165 sub-basins, each onecontributing to a stretch of river. Notably, buffer widths presentedvalues distinguished in classes, despite the variability in the meannitrogen influent for each sub-basin (Santin et al., 2016), a behav-ior that agrees with previous studies (Mander et al., 1997), as theoutput of nitrogen and phosphorus into streams was comparably


Fig. 6. Riparian buffer strip widths along the water bodies according to the ANNE.Extracted from Santin et al. (2016).

low despite the different input load. This illustrates the fact thatthe uphill part of the buffer vegetation retains a larger share ofthe nutrients, since the specific removal per meter is reported to

decrease downhill. It is worth noting that the largest width valuefrom the ANNE response, about 47 m, is rather close to the 50–60 mrange indicated by the authors in Mander et al. (1997). In fact, thevariability in ANNE buffer width was observed to depend moreheavily upon the vegetation cover type (VCT) and desired removaleffectiveness (RE). Regarding VCT, it was observed in Mander et al.(1997) that higher nitrogen uptake observed in younger vegetationmakes it more effective in nitrogen removal. This agrees with theresults of the ANNE, since it was observed that grass-forest regionswere identified as the areas less demanding of buffer width for thesame filtering effectiveness. From the training, validation and test,it was observed that the ANNs, and thus the ANNE, could capturethe effect of VCT. In this application, we use Landsat 5 images withresolution of 30 m, such that we approximate the RBS width to theclosest integer multiple, 60 m (Fig. 6).

Recalling the results presented in Santin et al. (2016), the totalvegetated area demanded by the ANNE for the filtering of 90% ofthe nitrogen in the watershed amounts 2.91 km2, well above thecurrent vegetated area and even above the legal demand. As weconsider the current watershed land use presented in Fig. 5 andcompare to the output of the ANNE, one obtains a picture of theRBS deficit. Indeed, the results indicate that there is a major areaof missing vegetation that amounts to 1.97 km2. An important andinteresting fact is that the area of missing vegetation according tothe ANNE is considerably larger (+0.81 km2) than would be requiredby the current environmental law in Brazil (1.16 km2).

Fig. 7. Results of the application of Enhanced Vegetation Index (EVI) to acquire initial and final conditions for the model: (a) original high-resolution true color image in theyear 2000 and (b) the corresponding EVI vegetation density in the year 2000 US Geological Survey (2000), (c) original high-resolution true color image in the year 2010 and(d) the corresponding EVI vegetation density in the year 2010 US Geological Survey (2010).


Fig. 8. Maps obtained during the model calibration process: (a) vegetation density obtained from application of EVI to the (right half of the) Landsat 5 image of the riparianforested area in the surroundings of Machadinho Dam, in the year 2010 US Geological Survey (2010) and (b) vegetation density obtained by means of numerical simulationof the DLG model, featuring the parameters ru = 0.03 and Du = 1.02 × 10−6.

Fig. 9. Maps obtained during the model validation process: (a) vegetation density obtained from application of EVI to the (left half of the) Landsat 5 image of the riparianforested area in the surroundings of Machadinho Dam, in the year 2010 US Geological Survey (2010) and (b) vegetation density obtained by means of numerical simulationof the DLG model, featuring the parameters ru = 0.03 and Du = 1.02 × 10−6.

3.3. Vegetation density for initial/final conditions

The initial and final conditions for the calibration of the modelwere obtained by means of the application of Enhanced VegetationIndex (EVI) to the Landsat scenes in US Geological Survey (2000,2010). The results are shown in Fig. 7.

3.4. Calibration and validation of the model

The model was calibrated and validated on the basis of twoLandsat 5 images. The images display a portion of the riparianpreservation area surrounding Machadinho dam reservoir and theyshow the same region in 2000 and 2010 for the same month of theyear US Geological Survey (2000, 2010) scenes. For calibration andvalidation of the model, we divide the images in two and use theleft-half for calibration and the right-half for validation. The cali-bration process searches for the couple of parameters Du, ru thatminimizes the error between the real and simulated final condi-tions on vegetation densities. The search was conducted over theparameter space Du × ru by successively increasing the resolution

around points leading to minima from coarser levels of grid resolu-tion. In the end of the process, the validation and calibration errorscalculated by means of RMSE, were ecal = 0.080 and eval = 0.097. Theresults from calibration and validation are shown in Figs. 8 and 9,respectively.

3.5. Application of the model

The model was applied to simulate forest regeneration 40 yearsahead in the region of the Ligeiro River watershed. To define thewidth of the RBS for each stretch of river in the watershed, weconsidered the results obtained from the ANNE in Section 3.2. Theinitial conditions were derived from the application of EVI to thevegetation belonging to the RBS applied to a satellite image fromthe watershed (US Geological Survey, 2016). The actual mesh wascomposed of 4300 points. The initial conditions of the simulationare presented in Fig. 10, while the results for 10 years, 20, 30 and 40years are shown in Fig. 11. It can be observed from Fig. 11-(d) that,except for some few spots, the RBS is expected to be in an advancedstage of regeneration. The largest growth rate was observed in the


Fig. 10. Current condition of forest density in the RBS of Ligeiro River watershed, obtained by means of application of EVI to the Landsat scene in US Geological Survey (2016)(a) 10 years, (b) 20 years, (c) 30 years, (d) 40 years.

first 10 years. The evolution of forest density along the period canalso be seen in the density histograms in Fig 12 .

3.6. Sensitivity analysis

Sensitivity analysis of the model with respect to the parametersshowed that the diffusive-logistic growth model is most sensitiveto the growth rate parameter, ru. The results of sensitivity analysisin Fig. 13 also reveals that the model can handle uncertainty ofabout 10% in the value of ru around the calibrated value withoutsignificant changes in the value of RMSE.

4. Discussion

4.1. Land management and ecology

Forest regeneration is a long-term process whose outcomedepends in a considerable extent on the management techniquesto be employed. The fact that management strategies can beimplemented and tested in models before they are implementedin practice can help enhance outcomes towards higher successrates in forest regeneration projects. Thus, the outcomes of theforest growth model can provide valuable information for land

management, such as forest growth rate, the expected vegetationdevelopment status over time and the anticipation of the likelyeffects of forest management practices. Further, the results can betailored for each specific location by means of accessible designparameters to be chosen according to requirements on removalefficiency (RE), mean nitrogen inflow (MNI) and vegetation covertype (VCT). In regard of watershed management, forest regenera-tion models can provide valuable input data for groundwater andsurface-water models in what concerns the effects of vegetationon water quantity, quality and dynamics. The relationship betweenforest, discharge, the underground flow and the recession in a basincan be observed in a number of papers. The research carried outin Tague and Band (2001) evaluated the discharge behavior of awater body in a forested area, thus demonstrating that the accu-racy in water balance analysis is improved when this relationshipis considered. Towards that, the author considers the coupling ofmodels in which rainfall, radiation, temperature, soil moisture,canopy behavior and evapotranspiration are taken into account inorder to determine the outflow of the basin in the water balance(Tague and Band, 2001). In turn, the paper in Foley et al. (1996) pre-sented the status of the relationship between soil occupation andwater balance, plant cover and water quality (Tiktak et al., 1995), aswell as its relation to surface and underground movement of water


Fig. 11. Simulation results to forest density in: (a) 10 years, (b) 20 years, (c) 30 years and (d) 40 years to RBS in the Ligeiro River watershed.

(Gerten et al., 2004; Tague and Band, 2001). In the studies of Móriczet al. (2010) the relationship between water loss due to interceptionand evapotranspiration is evaluated considering vegetation coverand its influence on the recharge process. Although the relation-ships between water balance, water availability, recharge, waterquality, recession, movement of groundwater and surface water,level of the groundwater table to forests are accepted (Smerdonet al., 2009; Peck and Williamson, 1987; Sivapalan et al., 1996),the coupled modeling of forest, groundwater and surface-waterseems rather unexplored from the viewpoint of physically-basedcoupled models. From an ecological viewpoint, the design param-eters can be chosen on the basis of desired biomass production,temperature regulation, water filtration, erosion and flood control,for instance, in order to protect biotic and abiotic components ofan ecosystem. We recall that, to a great extent, the restoration andregeneration of ecosystems is closely related to the regeneration ofthe its vegetation and forest cover.

4.2. Artificial neural network ensembles and the forestregeneration model as complementary tools

It has been shown recently that artificial neural networkensembles can be a responsive approach to black-box-model envi-ronmental phenomena (Santin et al., 2016). This is particularlyrelevant as the amount of measured data from environmental vari-ables steadily grows with the increasing availability of unexpensivesensors and data storage devices. Further, regarding environmentalprocesses depending on a large number of variables, the modelingbased solely on physical laws and equations becomes impractica-ble in most cases due to the large number of parameters involved.In this sense, the application of artificial neural networks can be of

Fig. 12. Histograms of forest density resulting from numerical simulations: (a) 10years ahead, (b) 20 years ahead, (c) 30 years ahead and (d) 40 years ahead.

value to provide a model to those parts of the process that are nottotally understood in terms of their constitutive physical, chemi-cal or biological relations. In this context, the conceptual model (asit is the case with the diffusive-logistic forest regeneration model)can be fed with consistent inputs from the data-based black-boxmodel. Thereby, emphasis is given to the process of interest, i.e.,the process of forest regeneration.


Fig. 13. Sensitivity of error to the model parameters.

4.3. Strengths and limitations of the results

The thorough application of the proposed methodology pro-vides three main results of importance in the context of forestgrowth and regeneration projects: (i) prognostic maps of for-est density; (ii) forest growth and diffusion parameters and (iii)performance-oriented RBS widths. A major strength of the resultsis that they are strongly based on data. Both the machine learn-ing and the physical description of forest growth strongly rely oncalibration, validation and test against data. Further, the ANNEallows flexible choice of input parameters type, which consider-ably extends the applicability of the methodology to the caseswhere other input variables (not necessarily those considered inthis paper) are available. A strength of the implementation is itprovides fast and effective tool for the solution of the model in anyordinary office computer with a CUDA GPU card. We remark thatthe parallel implementation achieves up to 50-fold speedup com-paratively to the serial implementation. We shall provide detailson performance in a separate paper. A limitation of the results thatcome as a result of the DLG model is that any subjacent dynamicsother than diffusion and logistic growth are not captured by themodel. For instance, slower vegetation growth might be observedin a hillslope that is subjected to erosion while faster vegetationgrowth might be observed in a hillslope with favourable solar orien-tation. As a consequence, it might happen that forest density mapsoutput by the model might contain inaccuracies as compared toreal scenes, especially as such unmodelled processes become ratherrelevant in a given scene/time window. This issue can be properlyidentified by means of the in loco validation of the geoprocessingof the scene.

5. Final remarks

The importance of forest modeling relates to a series of factors.First, there is the need for effective forest management decision-making, which can be enhanced as the future results of currentmanagement scenarios can be projected. This seems to be par-ticularly important as forest regeneration is a long-term process,which makes the costs and losses associated to uneffective prac-tices and unanticipated effects potentially substantial, since theycan extend for decades. Knowing the dynamics of intrinsic natural

recovery is an important step to assessing the potential of resourceconservation. The characterization and understanding of the typi-cal forest regeneration process are arguably relevant in the designand evaluation of preservation projects. This research presenteda self-contained framework intended to enhance and sharpen theunderstanding of forest regeneration and aid the design processby providing prognostics of the status of vegetation for years ordecades ahead.

All the computer codes and routines developed during thisresearch project are written in open platforms and available fordownload at modelagemambientaluffs.blogspot.com.br.

Acknowledgements

The authors thank FAPERGS (grant no. 002073-2551/13-1) andCNPq (grant no. 460329/2016-6).

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Declaração de Autoria

Declaramos que o artigo intitulado Modelling forest regeneration for performance-oriented riparian buffer strips bemcomo o conteúdo contido naquele texto e apresentado como trabalho de conclusão de curso por Luiz Augusto Richit,como parte das exigências para obtenção do título de Bacharel em Engenharia Ambiental e Sanitária é de autoriapessoal, juntamente com os demais autores segundo expresso na identificação de autoria do próprio artigo, o que podeser verificado através da versão final apresentada neste texto e sob a orientação de José Mario Vicensi Grzybowski .


Aluno: Luiz Augusto Richit

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