Keywords

1 Introduction

The Land Change Modeler (LCM) was developed (Eastman 2006) as an empirically parameterized land change projection tool to support a wide range of planning activities. Based on an analysis of historical land cover change, the system develops an empirical model of the relationship between land cover transitions and a set of explanatory variables. Mappings of future change are then based on this empirical relationship and a projection of quantity derived from a Markov Chain. The result is a business-as-usual (BAU) projection of change without subjective intervention. It is designed to support applications with strict BAU baseline needs such as REDD (Reducing Emissions from Deforestation and forest Degradation) climate mitigation projects.

2 Description of the Methods Implemented in the Model

At present, three separate empirical model development tools are provided in LCM: a Multi-Layer Perceptron neural network (MLP), Logistic Regression (LR) and SimWeight (SW). The MLP procedure is the default, and is the most mature and primary focus of LCM (Fig. 1). MLP is also the only procedure that can model multiple transitions at the same time. Logistic Regression is provided primarily for pedagogic reasons while SimWeight is an experimental machine learning procedure based on a K-Nearest Neighbor variant (Sangermano et al. 2010). In each case, analysis of two land cover layers in the recent past is used to train and evaluate the model.

Fig. 1
figure 1

In LCM, the process of land change modeling is organized into major stages embodied by tabs in the interface. The most important stage is that in which empirical models are developed relating historical changes to explanatory variables. In this example, the default Multi-Layer Perceptron Neural Network is used to develop transition potential maps (small maps, upper left)—empirically derived statements of the potential of land to undergo specific transitions. These are used in the subsequent change prediction tab to generate both future scenarios (large image, center) and maps of vulnerability to change (upper left)

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2.1 Training

For the Multi-Layer Perceptron, LCM examines each of the transitions over the historical period to determine the number of pixels that went through the transition being modeled (change pixels) and the number that were eligible to, but which did not (persistence pixels). The user is then required to specify the sample sizes to use for training the model. For MLP and SimWeight, equal-sized samples of change and persistence are required. However, the default sample sizes are very different—10,000 for MLP and 1000 for SimWeight. The difference relates to how they are used—for iterative learning in the case of MLP and characterization for SimWeight. For Logistic Regression, the sample chosen is proportional to the relative number of change and persistence pixels for the individual transition being modeled. The user is able to indicate the sampling proportion (the default is 10%) and the method of spatial sampling—stratified random sampling (the default) or systematic.

2.2 Simulation

In LCM, the simulation proceeds in three stages. The first is the development of transition potentials—mappings of the readiness of land to go through each of the transitions under consideration. The second is the estimation of the expected quantity of change and the third is the spatial allocation of the estimated change based on the transition potentials.

Transition Potentials

A transition potential is a continuous value from 0–1 that expresses the relative potential of a pixel to transition from one state to another. The metric varies from one empirical modeling procedure to another but in the final stage of the simulation, only the relative value of the metric matters.

If MLP is used as the modeling procedure, the transition potential is the activation level of the output neurons which represents the posterior probability of transition under an assumption of equal probability of change/persistence. With Logistic Regression, the transition potential is the probability of change assuming an identical quantity to that which transitioned during the historical period. With SimWeight, the value is unitless, but monotonic with the posterior probability of transition.

Estimation of the Quantity of Change

In the second stage, a Markov Chain analysis is used to determine the quantity of change for the forecast date selected. A Markov Chain assumes that the rate of change (but not the quantity of change) remains constant over time. The calculation proceeds (Eastman 2014) by first computing a cross tabulation of transitions between the land cover maps for the two historical dates. From this, the basic transition probability matrix (X) is calculated. If the date being projected forward is an even multiple of the training period, then the new transition probability matrix is calculated through a simple powering of the base matrix (Kemeny and Snell 1976). For example, if the training period is from 2002 to 2011 (9 years) then the transition probability matrix for 2020 from 2011 (9 years forward) is X1, for 2019 (18 years forward) is X2, for 2047 (36 years forward) is X4, and so on. However, if the projected time period is in between even multiples of the training period, then the power rule is used to generate 3 transition matrices that envelop the projection time period (if the 3 time periods are times A, B and C, the period to be interpolated will be between A and B). The three values at each cell in the transition probability matrix are then fed into a quadratic regression (thus there will be a separate regression for each transition probability matrix cell). Given that a quadratic regression (Y = a + b1X + b2X2) has 3 unknowns and we have three data points, it yields a perfect fit. This equation is then used to interpolate the unknown transition probability. From these transition probabilities, the projected quantity of change is determined for each transition being modeled.

Spatial Allocation

Given a set of transition potential maps and the projected quantity of change for each transition, LCM then allocates change based on a greedy selection algorithm. The greedy selection is based on the simple assumption that the areas with the highest transition potential will always transition first. Because a single pixel may be selected for multiple transitions, a competitive strategy is used whereby it will be assigned to the transition with the highest marginal transition potential. This will lead to some transitions being allocated less than the expected quantity of change. Thus the procedure iterates through a process of selecting pixels with lower transition potentials until all transitions achieve their required quantity.

LCM recognizes that some explanatory variables may be based on land cover, and thus change as transitions progress. For example, a model focused on deforestation may use a variable of proximity to existing agriculture. As agriculture expands, this variable will constantly be changing. Such variables are termed dynamic as opposed to static. Thus the user has the ability to predict in stages with dynamic variables being automatically recomputed at each stage. The procedure chosen for re-computation can be as simple as a single distance calculation to a complex macro. For example, a user may have empirically determined the potential for transition based on the age of the forest post-agriculture, and thus may use the macro option to add time and then re-compute the transition potential at each step.

2.3 Validation

Validation is handled differently for each of the empirical modeling procedures. For MLP, half of the training data are reserved for validation. Validation is a critical component of the training process. At each stage in the training, learning is refined with one half of the data and the quality of the model is assessed by comparison with the other half. Accuracy and model skill over all transitions and persistences combined are dynamically reported during the training process. Model skill is reported as a Heidke Skill Score (Heidke 1926), also known as Kappa (Cohen 1960), which ranges from −1 to +1 with 0 indicating a skill no better than random allocation. At the end of the empirical modeling procedure, LCM provides a detailed accounting of accuracy and skill for each transition and each persistence category. It also provides a wealth of information about the contribution of each variable to the model including a backwards stepwise assessment that allows for a very easy determination of the most parsimonious model.

For SimWeight, again, 50% of the training data are reserved for validation. From these, a Peirce Skill Score (Joliffe and Stephenson 2003) is evaluated—a value similar in nature to a Heidke Skill Score in that it ranges from −1 to +1 with 0 representing the point where the hit rate and false alarm rate are equal. SimWeight also reports the relevance of variables by examining the variability of a variable within historical samples of transition relative to all areas (Sangermano et al. 2010).

For Logistic Regression, validation is handled by a Goodness of Fit measure which expresses the degree to which the fitted values of the modelled regression match the training data. Relevance of variables is assessed by the slope coefficients and t-score values, although use of standardized variables is recommended for this purpose.

2.4 REDD

An important application of this kind of empirically-modeled projection tool is the climate change mitigation strategy known as REDD—Reducing Emissions from Deforestation and forest Degradation. To meet the special needs of these programs, LCM provides a special set of tools for the development of REDD projects. Tools provide for the definition of the project and leakage areas, specification of carbon pools to be considered, method of calculation and carbon density in the evaluation of CO2 emissions. Non-CO2 emissions are also considered. Leakage, success and effectiveness rates are then specified for each of the reporting stages. In the end, 19 tables are produced following the BioCarbon Fund methodology. However, these are easily re-formatted into any of the prevailing approved methodologies.

3 Applications

Land Change Modeler has been evaluated and applied across many disciplines in varied geographic areas since its release in 2007. It has been evaluated against other land change methods (Eastman et al. 2005; Fuller et al. 2011; Mas et al. 2014; Paegelow and Camacho Olmedo 2008). LCM has been applied to forest monitoring and deforestation (Khoi and Murayama 2011; Valle Jr et al. 2012) and its impacts on biomass (Eckert et al. 2011; Fuller et al. 2011; Saha et al. 2013), biodiversity (Dean and Salim 2012; Uddin et al. 2015) and species habitat impact assessment (Fuller et al. 2012). LCM has even been employed to model post-socialist land change in Eastern Europe (Václavík and Rogan 2010). LCM is an accepted tool by the Verified Carbon Standard (VCS 2014) and is extensively used in REDD (Areendran et al. 2013; Centro de Conservación 2012; Kim and Newell 2015) and REDD+ project planning (Moore et al. 2011; Sangermano et al. 2012; Scheyvens et al. 2014; VCS 2014).

4 Final Considerations

LCM has now been in public use for more than a decade. It was commissioned by Conservation International and the conservation community still constitutes the largest body of users. Companion software components have been developed to work closely with LCM including the Habitat and Biodiversity Modeler and the Ecosystem Services Modeler. Development of LCM continues with two new machine learning procedures (Weighted Normalized Likelihoods and a Support Vector Machine) currently in testing. Additionally, a cloud-based implementation is currently under development. Given the pace of anthropogenic land conversion, the ability to develop defensible and skillful land change models is of critical importance.