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Using local saturation

Load the model “simulate_deforestation_using_local_saturation.xml” from \Examples\advanced\local_saturation Local saturation prevents a change from occurring within a specific region, in which a class area is greater than an established threshold (figure bellow). This feature is useful to simulate diffusion process as well as to establish a minimum forest remaining area (as established by the Brazilian forest code for private properties). Local saturation can be implemented by reducing the probability of a transition using an asymptotic function as follows:

P2 = P1 * (Li – Oc) / (Li + Oc), case Li >= Oc
P2 = 0, case Li < Oc

where P2 is the new probability, P1 is the original probability, Li is the maximum number of cells of a particular class that is allowed to occur within a certain map neighborhood and Oc is the number of cells of that class within that neighborhood. In this example, deforestation must stop in a local region (in this case a window size of 59.25 hectares or 9 cells - 3×3 window) when 50% of this region is deforested. For each model step, the amount of deforested cells is calculated in every 3×3 window of the landscape map. In this case, the threshold consists of five cells as follows:

P2 = P1 * (5 - Oc) / (5 + Oc), case Li >= Oc
P2 = 0, case 5 < Oc

Two landscapes without and with local saturation effect

Three Calculate Map functors are added to a deforestation simulation model in order to incorporate the saturation effect. Open them to see their equations. The first one assigns “1” to deforested cells and “0” to forest. The second counts the amount of cells deforested within a window size 3×3. It uses a neighborhood operator as follows:

nbCount(i1, 3, 3)