Abstract
The forests of the Amazon arguably represent the single-most reported upon ecosystem globally, with the “Arc of Deforestation” having captured scientific and popular attention. Critiques establishing deforestation as a myth present evidence of an incomplete if not erroneous assessment of forest processes as interacting within larger institutional and climatic systems. As remote assessments of deforestation or reforestation may be strongly dependent upon the seasonality of input images, this work brackets the potential range of forest-change findings by running graph automata simulations while varying forest cover inputs. Results confirm that model results are quite sensitive to input amounts of forest cover as small as those detected even in one intra-annual cycle previously. These findings are interpreted in light of the seasonality of previous work throughout the Amazon and suggest that the overestimation of deforestation may be systematically underestimating reforestation processes at work in the Amazon.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
9.1 Introduction
Global afforestation/reforestation/deforestation (ARD) rates remain a highly contested sphere (Grainger 2008; Grainger, this volume, Chapter 2), with discrepancies across regions, studies, and time periods. Ostrom and Nagendra (2006) in assessing integrated satellite/field/lab studies point out that incongruities in findings should trigger greater scrutiny, just as coherence among findings should be read to increase trust in those findings. While that point was made in regard to differences in studies across spatial scales, the same can be applied to studies in different localities and across differing temporal scales (in terms of temporal grain or timing and temporal extent or study period). For a period in the scientific literature, it appeared that, particularly in tropical forests, there was a consensus as to the presence of deforestation (whether complete or thinning) (e.g., Skole and Tucker 1993; Turner et al. 2004) and the major research efforts were aimed at assessing the rates of loss (e.g., Achard et al. 2002) and understanding the proximate and ultimate driving factors behind those losses (Turner et al. 1995; Laurance 1999; Geist and Lambin 2002; Nagendra et al. 2003).
Near the end of this period the focus followed that of more general landuse/landcover change studies and bifurcated to include a strong emphasis on simulation and scenario modeling (Clarke et al. 1997; Clarke and Gaydos 1998; Verburg et al. 2004; Batty 2005; Andersson et al. 2006; Walsh et al. 2006). Though the challenges in these studies were well understood (Rindfuss et al. 2004; Grainger 2008), issues remained with validation, particularly of historical, remotely assessed components (Brown et al. 2005; Pontius and Malanson 2005). But few until this volume stopped to question whether the underlying assumptions regarding deforestation and nearly ignoring the possibility of reforestation (or afforestation) are justified (see especially Nagendra and Southworth, this volume, Chapter 1). Given the changes in forest policy that appear to be moving towards supporting reforestation efforts (Butler and Laurance 2008; Rudel 2008; Rudel, this volume, Chapter 3), it appears salient to now investigate previous findings, models, and methods.
Considered the leading effort at a global forest inventory, the FAO’s Forest Resources Assessment and related reports are used by policymakers, managers, and researchers from around the world (FAO 2001, 2005). In order to complement field- and office-gathered statistics on forest inventory, the FAO utilizes satellite imagery for synoptic assessments. In the 2000 assessment, the FAO improved upon the 1990 report by using a triplicate of images to compare forest changes from 1980 to 1990, 1990 to 2000, and the overall period of 1980 to 2000. In doing so, they reported important issues remaining to be resolved including, notably, that comparable time-series were absent in most countries included in the assessment. Overall figures estimated global forest losses at 9.2 million hectares in the 1980s, with a reduction in losses in the 1990s totaling 8.6 million hectares. Losses in closed forest went from 8.0 million hectares in the 1980s to 7.1 million hectares in the 1990s. But the report goes on to indicate that since the standard error rate was 15%, the end result of this report as to whether there had been a net increase or decrease was not statistically significant. Given the overall inventories of 3.9 billion hectares of forest in 2000 (with net and gross deforestation annual rates of 9.0 and 13.5 million hectares respectively), this lack of confidence perhaps offers some optimism in their finding of an annual increase in forest cover of 4.5 million hectares.
Again, difficulties in assessing, interpreting, and comparing ARD rates is increasingly well documented (Grainger 2008), and much of the problem has been acknowledged by the remote sensing community some time ago, with particular attention paid to difficulties in assessing age groups of forest in fast-growing tropical forests (Foody et al. 1996). The smaller the sample used also can bias findings, particularly depending upon how those samples were collected. The FAO was advised to use 350 samples but due to budgetary constraints was limited to 117 sampling units for the triplicate pan-tropical remote sensing survey (FAO 2001). Ultimately 113 sites were used because of difficulties in finding archived, cloud-free imagery. Compounding difficulties in assembling the time series for each sample unit was also the issue of image seasonality, important even in the oft-considered “aseasonal” tropics (McCleary et al. 2008).
While early assessments of deforestation were aspatial, the vast majority of current deforestation studies rely upon from-to change detection. The underlying premise of a change detection approach is that the start and end year are compatible. In remote sensing terms, the term “anniversary date imagery” is used, meaning that, for example, one should only compare changes across time when seasonal variations have been excluded. For example, in a temperate coniferous forest, it would be improper to compare a summer (“leaf-on”) 1975 image with a winter (“leaf-off”) 1995 image, since some amount of seeming deforestation would be [incorrectly] detected by comparing asynchronous imagery. In many temperate latitudinal ecosystems where seasons are clearly demarcated and cloud cover is less commonly an issue, obtaining change detection image pairs in the same season can be relatively straightforward. But move toward the equator to the tropics, and the issue becomes cloudier, literally.
9.2 Conceptual Framework
Simulation models are increasingly used to forecast land use and land cover change (LULCC) generally and forest change specifically (Rindfuss et al. 2004, Verburg et al. 2004). As with any model, deterministic or stochastic, outputs may vary widely with slight changes in inputs (Wolfram 1984). Such is particularly of concern with spatial simulation models, where input variations can have multiplicative effects when neighbourhood interactions compound the effects of different inputs as translated through transition rules (Brown et al. 2005; Pontius and Malanson 2005). Modeling dynamic systems can thus present difficulties when picking base year or input images. While the Amazon is certainly regarded as a highly dynamic system, in fact much of the narrative of the greater Amazon centers on deforestation (whether complete conversion or thinning) studies, many of which take place in the eastern Amazon where seasonal variability is not as great an issue (Moran 1993; Gerwing 2002). But recent work in the western Amazon has documented strong seasonal pulses not just in precipitation and flooding, but in observable vegetation and forest cover change, potentially associated with green-up events (McCleary et al. 2008). Given the recent climatic oscillations resulting in seasonal drought and even burning of rainforests (Laurance and Williamson 2001; Tapley et al. 2004; Wright 2005), it is even more important to understand how these seasonal shifts may impact deforestation simulation results. This work follows on intra-annual assessments in the northern Peruvian Amazon (McCleary et al. 2008), using graph automata (a generalized form of cellular automata) (Sarkar et al. 2009) to assess the sensitivity of modeling results of forest cover change to randomized discrete intervals of change (increase and decrease) in forest cover.
This work is positioned in the Peruvian Amazon. Like much of the tropical Amazon, the area is riddled with cloud cover year-round, rendering image acquisition difficult without regard to seasonality. And in comparison to her eastern/Brasilian counterparts, the Peruvian Amazon has been reported to be relatively aseasonal, lacking the distinct wet and dry seasons that Brasil rainforests experience. Despite this, vegetation greenups have been preliminarily reported that in fact suggest the need for caution in overlooking seasonality in any of the Amazonian forests long described by narrative of extensive deforestation (McCleary et al. 2008). This work thus seeks to use this section of the northwestern Amazon as a case study to understand how, even in the most presumably aseasonal environments, seasonal vegetation changes can radically impact assessments of change detection, particularly with respect to vegetation and especially with respect to forest cover. Moreover, since a simulation modeling approach is employed, this research also provides information on how the selection of input data can bias results to find more or less change in a particular land cover, such as forest. Lastly, because seasonality is so commonly overlooked in many tropical remote sensing studies (to be fair, the cloud cover issue prevents many researchers from even having the chance to assess seasonality in a given calendar year), this chapter concludes by questioning whether the predominant narrative of tropical deforestation is, in some part, a predictable if previously undescribed bias stemming from ignoring seasonality in tropical forest ecosystems.
9.3 Discussion of Methods
9.3.1 Cellular Automata
Cellular automata are discrete dynamical systems that evolve over discrete time steps (Toffoli and Margolus 1987). They have been applied widely in geography to study land use and land cover change (Malanson et al. 2006a; Manson and O’Sullivan 2006; Walsh et al. 2006). Studies have used cellular automata to simulate urban (Clarke et al. 1997; Clarke and Gaydos 1998; Batty 2005; Andersson et al. 2006; Torrens 2006; Xie et al. 2007) and rural development (Malanson et al. 2006b). Cellular automata are composed of sets of spatially distinct cells in a grid system, where the spatially explicit nature facilitates local interactions between the cells. In addition to its location, each cell is assigned one of a finite number of states. At each time step, these states are updated on the basis of both the present state of each cell and the states of the cells that fall within a selected radius. The system as a whole thus evolves on the basis of the evolution of the states of its component cells. Though the individual components are thus quite simple, their interaction allows cellular automata to represent complicated dynamic phenomena (Wolfram 1984) which may then evidence emergent properties of complex systems (Malanson 1999; Manson 2001; Walsh et al. 2006). Formally, a cellular automaton is a graph G = (V, E) in which V consists of a finite set of vertices and E consists of a set of pairs of vertices such that for each (v i , v j ) ∈ E, both v i ∈ V and v j ∈ V and if (v i , v j ) ∈ E then (v j , v i ) ∈ E (Harary 1969). As applied to the models considered in this chapter, the vertices in G represent cells within a given landscape, while the edges in G represent causal interactions between pairs of cells.
One of the limitations of a cellular automata approach is undue restrictions such as requiring adjacency for cells to impact one another (Gutowitz 1991; Sarkar et al. 2009), despite the acknowledgement in the land use literature that many types of land use changes are in fact triggered by states and events of specific distal areas (Turner et al. 1995). Releasing this restriction adds computational complexity but improves the ability of a model to represent real-world processes.
9.3.2 Graph Automata
While cellular automata are sufficiently general to allow for their application to a number of different modeling problems, assumptions implicit within their mathematical framework prove limiting. As noted above, cellular automata models assume both: (i) each cell is subject to the same set of transition rules and (ii) the transition of each cell depends upon the states of all cells that are located within a uniform radius (Toffoli and Margolus 1987; Gutowitz 1991). When applied to the study of LULCC, each of these assumptions can prove to be prohibitive. One way to overcome this limitation is through the use of a more general mathematical structure to represent cellular interactions. Graph automata offer such a structure by allowing for the representation of potential interactions between any set of cells, regardless of their location (proximity) in space (Boccara 2004). Rather than an undirected graph, in which the effects of v i on v j are mirrored in those of vj on vi, graph automata are directed graphs in which such symmetry is not required. In addition, the set of rules used to determine the transitions from one state to another need not be identical for each cell. By connecting the cells of cellular automata in a complex network, rather than on a regular geometric grid, graph automata thus offer a more general mathematical framework than that provided by cellular automata (Burks 1970; Gutowitz 1991). Though graph automata were introduced more than 30 years ago (Rosenstiehl et al. 1972, Ng et al. 1974; Milgram 1975; Smith 1976; Wu 1978) they have been used only rarely to model empirical phenomena. It should be noted that while “graph automata” is the name most frequently use to refer to these mathematical structures, they have also been referred to as intelligent graphs (Rosenstiehl et al. 1972), polyautomata (Smith 1976), and web automata (Shah et al. 1973; Milgram 1975). Sarkar et al. (2009) provided the first application of graph automata to the study of LULCC in both the Peruvian Amazon and Andes. To the best of our knowledge, this paper represents the second such application.
9.4 Case Study
9.4.1 Study Area
The study area spans the Iquitos, Peru area (centroid 3.74º S, 73.26º W), the largest city in the western Amazon at over 400,000 people, and its upstream associated peri-urban, agricultural, and forested areas. Notable about this area is the lack of overland connection to Lima or Brasil; while roads are used to move goods and people in the area, in general the city is considered to be riverlocked and dependent upon the Amazon (just north/downstream of the confluence of the Marañon and Ucayali Rivers) for transportation. The limited accessibility of the area is likely to affect the dynamics of LULCC as such a relationship has been found elsewhere in the past (Nagendra et al. 2003). The area is comprised of floodplains, ancient floodplains, and slightly upland areas noted for their heterogeneity in soils ranging from white sands to red clays and associated with blackwater and whitewater systems, respectively (Tuomisto et al. 2003; Crews-Meyer 2006).
9.4.2 Data
This study used estimates of landcover derived from a Landsat 7 ETM+ scene (WRS2 Path 006, Row 063) acquired May 31, 2001. The original landcover extraction of this scene as compared to other intra-annual images (March 12 and September 20, 2001) with concomitant accuracy assessments was reported previously (McCleary et al, 2008). The overarching finding of McCleary et al (2008) was that even in supposed “non-seasonal” environments such as the tropical northwestern Amazon (which in contrast to the Brasilian Amazon has no marked dry season), there is fact is a strong seasonal pulse detectable among a variety of landcover classes, including forest cover. Because longer-term change detection studies rely upon a presumption of intra-annual stability, this seasonal/cyclical change in fact may obscure true change estimates when anniversary imagery is unavailable. Sarkar et al. (2009) used a subset of the Iquitos classifications to model future landcover and landuse change under a scenario of increased urban and agricultural expansion in this riverlocked area. This research also used the subset of the May 31, 2001 Path 006 Row 063 classification centered most closely on Iquitos but including a variety of forest and agricultural areas in order to understand the importance of input imagery into the modeling process. Of the three images used in intra-annual comparison in McCleary et al. 2008, the May 31st image had the least cloud cover that can present problems in spatial simulation modeling. Thus this image was used in analysis here. That is, in cloud-ridden areas such as the Amazon, it is highly unusual to have multiple cloud-free (or low cloud cover) scenes per year; what then are the consequences for a/de/re-forestation research if the scene chosen represents a seasonal shift in greenup that is inappropriate for use as a baseline in longer-term change detection studies?
To this end, the same subset used in Sarkar et al. (2009) was employed here for computational tractability, having an area of 754,961 ha and modeled as a set of 8,612,624 cells. From these, 224,158 cells (roughly 2.6%) were removed from analysis due to cloud cover.
9.4.3 Methods
Graph automata were used to model land cover change in an Amazonian landscape classified using a hybrid unsupervised-supervised approach with Landsat ETM+ imagery (McCleary et al. 2008). While original classification work used a Level-2 classification, here a Level-1 classification was used to ensure comparison with previous work (Sarkar et al. 2009) and to better fit transition rules derived from observations over multiple field seasons and informed by household interviews. An overview of the modeling process is shown in Fig. 9.1. Each vertex in the graph automata represented a 900 m2 cell (30 m pixel). A simple topology was then used to determine the edges of the graph. An edge of weight one was used to connect each pair of physically contiguous cells. Edges of weight two were then used to connect each cell to the set of cells physically contiguous with those to which it was connected with an edge of weight one, and to which it was not yet connected. This process was repeated until edges had been defined for each pair of cells. The resultant assignment of edges to the cells allowed for the representation of the physical distances between cells, with the weight of an edge equal to the distance between the centroids of the cells, as measured in 30 m increments. States were assigned to the cells so as to represent their initial occupation of one of the following states: (i) Forest; (ii) Agriculture; (iii) Water; or (iv) Urban/Bare.
In addition to the original landscape, two additional landscapes were produced by modifying the number of forested cells in the original landscape. In one such landscape, the total number of forested cells was increased by 10% of the initial number of forested cells. Cells that were originally Agriculture or Urban/Bare were randomly selected for conversion, with the probability that each such cell was converted equal to that required for the expected number of forested cells to increase by 10%. Analogous methods were used to create the other landscape, in which the number of forested cells was decreased by 10% from the initial number. The creation of these landscapes allowed for the investigation of the effects of the initial degree of forest cover on the dynamics of the landscape change. Though increases or decreases in forest cover would not occur completely randomly on the landscape, random assignment was used to avoid introducing unnecessary bias and/or path dependence by assigning states through another means (e.g., intentional placement or simulation).
Following the creation of these modified landscapes, a series of simulations was performed to study the evolution of forest cover in both the original and modified landscapes. In these simulations, the status of each cell in the landscape was updated stochastically, with probability distributions informed by both the current state of the cell and the states of the cells around it. A set of cells was defined as “contiguous” if an edge of weight one connected each cell to at least one other cell in the set. Contiguous sets of cells thus represented spatially clumped sets of cells. The transition rules used to update the states of the cells were based upon the careful analysis of patterns of historical landscape change in the Amazon region (Sarkar et al. 2009). A summary of the transition rules is provided in Fig. 9.2. All transition rules were based upon multiple years of field observation (e.g., tracking how quickly the urban perimeter expands and under what conditions) as well as basic ecological processes for that area’s ecosystems and soil types (e.g., regrowth of early successional tree species such as cecropia as varies among soil types). A qualitative description of the rules follows.
Urban and Bare cells had to be grouped together for classification, but in relatively know proportion. Urban/Bare cells close to a cluster of similar cells tend to remain Urban/Bare. Otherwise, they tend to largely become agriculture (primarily the succession of Bare cells, though some Urban conversion has been noted). Due to shifting river flows, Urban cells have seen as taken over by the river, as have exposed Bare cells due to river meanders. Bare cells may also convert to forest roughly 20% of the time, and there have been traces of Urban reclamation into forest parks in the city center.
Forested cells close to small clusters of Agriculture convert to Agriculture at an observed rate of roughly 20% per year, while the rest tend to remain forest (this is without regard to topography or soil type, both mitigating factors in this undulating terrain, as noted by Tuomisto et al (2003)). Forested cells away from Agriculture but close to water may occasionally be converted to Urban (ports), Water (from river meanders), or Agriculture (floodplain farming), though usually (over 90%) stay Forested. Forested cells near neither Agriculture or Water clusters are urbanized (or at least cleared) at 10% per year, and undergo agricultural extensification at roughly 5% per year, with the rest remaining forested.
Agriculture cells on the periphery of Agriculture clusters tend to remain Agriculture. When not connected to other agricultural areas but connected to clusters of Water cells, they tend to convert to Water at 10% per year (river meanders), regrow into Forest at 40% per year (often because early successional growth is misclassified as agriculture), become cleared or converted to Urban occasionally at 40% per year, and stay Agriculture roughly 10% of the time for any given year. Agriculture cells not in proximity to Agriculture or Water cells often are converted to Urban/Bare or Forest (regrowth), and remain Agriculture over half the time.
Water cells connected to even very small clusters of other Water cells predominantly tend to remain Water in the following year, though very rarely (proportionately) may become Urban/Bare (ports, river meanders) or Agriculture (floodplain farming). An exception to this condition occurs if the Water cell is also connected to a large Forest cluster (usually flooded forest), in which case it will remain Water. Otherwise, in general Water clusters remain Water unless very rarely converted to Agriculture or are the result of river meanders that take more than a year to establish vegetation.
The rules were selected so as to represent likely annual changes in land cover. A detailed discussion of the considerations that informed the selection of these specific transition rules is provided in Sarkar et al. (2009). Computational approaches to transition rule selection have also been employed in the study of cellular automata (Li and Yeh 2004).
9.4.4 Results
Maps representing the different landscapes with which the simulations were initiated are provided in Fig. 9.3. In comparing Fig. 9.3a to Fig. 9.3b and Fig. 9.3c, the general differences in initial forest cover can be observed. However, the modifications depicted in Fig. 9.3b and c appear primarily as background noise and thus cannot be easily identified at the scale at which these figures are presented.
For the original landscape, the simulation was run 1,000 times at annual time steps for 15 years, while 100 simulations were performed for each of the modified landscapes. Transition matrices representing the frequency with which the cells changed from one state to another are provided in Table 9.1. In these matrices, the rows represent the initial states of the cells, while the columns represent the states of the cells after 15 time steps. Entry (i, j) in the matrix thus represents the percentage of cells that initially occupied state i and that subsequently occupied state j following the completion of 15 time steps. A different matrix was produced for each of the initial landscapes, with the comparison of these matrices thus allowing for the analysis of the effects of initial forest cover on the dynamics of forest cover change.
In addition to these transition matrices, the effects of the initial forest cover on the A run was selected randomly from the 100 runs performed using each of the altered landscapes. Maps depicting the landscape at the end of the fifteenth time step of each randomly selected run are provided in Fig. 9.4, with a corresponding subset for easier visual interpretation shown in Fig. 9.5 (a–e) over multiple conditions.
Figure. 9.4a depicts the simulation results starting with a landscape in which forest cover has been increased from that of the original landscape by 10%. In comparing this landscape with that of the original landscape, the primary differences lie in the formation of several small clumps of Agriculture and Urban/Bare cells. The formation of these clumps of cells follows as a consequence of the transition rules, which specify that connected sets of Agriculture and Urban/Bare cells will feed back upon themselves, thus increasing the number of Agriculture and Urban/Bare cells, as is seen in Fig. 9.4a. In contrast with the Agriculture and Urban/Bare cells, the Water cells are not predicted to be substantially altered over the course of the 15 year period. This result is likewise consistent with the transition rules, which indicate that connected sets of Water cells are likely to remain unchanged during the course of the simulation.
Figure. 9.4b depicts the simulation results starting with a landscape in which forest cover has been decreased from that of the original landscape by 10%. As can be seen, the loss of initial forest cover and the replacement of the Forest cells with Agriculture and Urban/Bare cells resulted in a substantial increase in the potential for sets of these connected cells to further transform the surrounding forest, thus generating the large clumps of Agriculture and Urban/Bare cells that dominate Fig. 9.4b. An initial decrease in forest cover can thus lead to substantial further decreases in the number of forested cells. The comparison of Fig. 9.4a with that of Fig. 9.4b thus indicates the potential magnitude associated with changes to the initial conditions of the graph automata. The use of initial conditions that differ in forest cover by only 20% can lead to substantially different simulation results. The importance of such variation to the study of LULCC stems from the propensity of seasonal variation to result in similar alterations of forest cover. For instance, past studies on the seasonal variation of forest cover in the Peruvian Amazon have found the forest cover to diminish by as much as 17.1% between the months of March and September (McCleary 2005). The changes in forest cover considered in this chapter are within the range of the observed changes (using a May image and synthesizing seasonal change, due to cloud cover limitations in the March and September imagery). The same model, using data drawn from different seasons, may thus produce substantially different results.
Table 9.1 indicates that the effects of increasing initial forest cover are nonlinear. Whereas only 45.81% of the initial forest cover was preserved in the original landscape, an increase in the initial forest cover by 10% resulted in the increase in this retention rate to 72.65%. In contrast, the decrease of the initial forest cover by 10% resulted in the retention of 45.70% of the initial forest cover, a retention rate quite similar to that associated with the original landscape. It thus appears that, in the landscape studied in this analysis, decreases in initial forest cover have only a limited effect on the dynamics of subsequent forest cover change, while increases in forest cover result in substantial changes to these dynamics. This type of nonlinear effect is characteristic of complex systems (Manson and O’Sullivan 2006). Further study of the transition rules proposed in this analysis will likely lead to the identification of additional interesting phenomena.
9.5 Discussion
9.5.1 Methodological Implications
The primary benefit of this approach is to improve the potential realism of modeling by releasing the restriction of adjacency for the interactions of cells, but this improvement comes at the cost of increased computational requirements that have in part restricted the scope of this analysis. Using only a subset of the area (754,961 ha) resulted in 8,612,624 cells; combined with a minimal classification scheme (only four classes) and run for only fifteen annual time steps, each run still took 128 min to complete on a Dell PowerEdge 2850 with a 2 GHz Pentium 4 Xeon CPU and 8GB RAM. The 100 simulations for the two input images with varying forest cover thus required more than 2 weeks to complete. Ideally, the work represented here should be repeated using a greater number of input images with smaller incremental change in each image in forest cover (e.g., in 1% increments instead of 10% increments). To test the robustness of those findings, multiple simulated landscapes at each level of forest cover should be used as well. Running a greater number of simulations obviously would produce an additive effect in processing time. A more realistic implementation of the model should also use a more detailed classification, but increasing the level of classification (to include more classes) and the resulting increase in transition rules would exponentially increase the computational complexity. Further, the generation of transition rules may be limited by increasing to that many classes. For instance, field interviews with local households may not be capable of providing such information if the respondents themselves do not view the landscape with the same “classification scheme” as needed for analysis, highlighting potential pitfalls and biases in original class definition (Robbins 2001).
Further realism could be introduced through the inclusion of the location of a cell as part of the function used to alter the initial landscapes. This step was avoided here so as to avoid bias that could propagate through the simulations, but is feasible and a benefit of a graph automata approach. Also, in this analysis, each forested cell was altered with the same probability: this is ecologically implausible. When changing the forest cover of the original landscape, forested cells selected for alteration were randomly changed to or from Agriculture and Urban/Barren. It is unrealistic to assume either that conversion to these two states should occur with equal probability. The probability with which forested cells are changed to cells of other types is likewise spatially dependent in a manner not captured in this analysis. The representation of spatial heterogeneity within models of land cover change will likely demand the application of different transition rules for different cells. Though the mathematical framework that we present in this paper makes possible the application of these different rules, the ascription of different transition rules to different individual cells will require the empirical analysis of the individual cells. This type of detailed study has not been made for use in this analysis, though the results of such a study could be easily incorporated into our framework. The addition of other “layers” of information (e.g., underlying soils, proximity to logging operations) would improve upon current results but would greatly increase the potential interactions between the cells, thus compounding the problem of computational complexity. In sum, cells are not differentiated to the full extent possible, and the present analysis does not make full use of the attributes of graph automata.
9.5.2 Methodological Implications
While subsequent analyses of the effects of forest cover on landscape change should examine the effects of altering these conditions to more fully realize the benefits of a graph automata approach, the findings here do provide a proof of concept and support the preliminary conclusion that variation in forest cover observed in one intra-annual time series classification can in fact yield marked differences in simulation results. McCleary et al. (2008) document that by comparing three classifications of images acquired over a span of 6.5 months, significant fluctuation of forest cover in and out of forest classes (particularly with agricultural and other herbaceous classes) occurred in amounts greater than tested here. These results thus show that intra-annual fluctuations are indeed problematic for selection of inputs to simulation models of deforestation and reforestation, and underscores the findings of McCleary et al. (2008) and others that a multitemporal (intra-annual) classification approach is critical for proper assessment of inter-annual changes (Walsh et al. 2001), and perhaps even more so for seeding simulation models that may often be highly sensitive to variations in input cover (amount and distribution) (O’Sullivan et al. 2006). While understanding that simulations are sensitive to changes in inputs (Wolfram 1984), this work provides empirical support of that sensitivity based upon observed (intra-annual) ranges in landscape response in the western Amazon, and suggests that simulation model results of Amazonian forest change be reconsidered in light of the timing of the input imagery.
The larger implications for disentangling past and future assessments of forest changes loom large, especially when revisiting the FAO report finding that, since their standard error was 15% and the net loss of forests was less than 15%, “findings” of deforestation may actually be findings of afforestation or reforestation. Such is not to suggest that all deforestation assessments have been grossly incorrect; rather, there are likely several forces at work which once adequately investigated will explain the discrepancies and provide a more nuanced understanding of ARD processes: (1) seasonal timing of input imagery: even in aseasonal environments, this work has shown that simulation outputs can vary greatly to seemingly small changes in forest cover input; (2) as the FAO reported, non-comparable time-series (e.g., comparing a 1985–1991–1999 triplicate to a 1986–1990–2000 triplicate) complicates interpretation of findings across sites; (3) as per Foody et al. (1996), successional stages can be difficult to assess with a high degree of accuracy unless proper methods are used and adequate field data exist; (4) using the greatest archival extent possible of satellite imagery entails multiple sensor systems and therefore multiple scales of observation, complicated by the multiple scales of ARD footprints that result from very different ARD processes (Foody et al. 1996), and running single-scale studies only may therefore miss important changes in forest cover and quality; (5) many simulation programs treat certain classes (e.g., urban) and certain processes (e.g., deforestation) as terminal – that is, there is no recovery possible in the hard-coded rules despite the fact that there exist many field-based (if anecdotal) mentions of pockets of urban reforestation, for example; and (6) the total range in annual deforestation rates reported for the Amazon alone spans more than the confidence interval. The beauty of simulation modeling is that it provides verifiable/falsifiable proof of the sensitivity of modeling inputs and parameters (e.g., decision rules); verifying the accuracy of the results of multi-temporal analyses remains problematic but critical (Pontius and Malanson 2005). It is hoped that this work and other similar efforts compels researchers to revisit, rerun, and reinterpret their own “deforestation” studies.
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Acknowledgments
Authors are grateful to collaborating team members Sahotra Sarkar for his help in the original formulation of the mathematical framework of the graph automata, Christopher D. Kelley for programming assistance, and Kenneth R. Young for overall field and project analysis and for the chapter photograph. Field assistance and classification work was aided by Amy L. McCleary and Mario Cardozo. This work was supported in part by a National Science Foundation Small Grant for Exploratory Research (SGER) and Doctoral Dissertation Improvement Grant BCS – 0623229 as well as by the GIScience Center at the University of Texas at Austin.
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Crews, K.A., Moffett, A. (2009). Importance of Input Classification to Graph Automata Simulations of Forest Cover Change in the Peruvian Amazon. In: Nagendra, H., Southworth, J. (eds) Reforesting Landscapes. Landscape Series, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9656-3_9
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