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--- tutorial:using_local_saturation [2013/07/24 15:24]
juliana
+++ tutorial:using_local_saturation [2013/07/24 15:40]
juliana
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 For each model step, the amount of deforested cells is calculated in every 3x3 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**
+[{{ :tutorial:advanced_21.jpg |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 3x3. It uses a neighborhood operator as follows:
+**nbCount(i1, 3, 3)**
+where nbCount is the neighborhood counting operator, i1 is map # 1, and 3,3 is the window size in cells. You could easily increase the neighborhood size, changing these values. Then, a third Calculate Map is added to apply the local saturation rule on the probability map as follows:
+**if v1 - i1 >= 0 then i2 * (v1 - i1) / (v1 + i1) else  0**
+Where v1 is the saturation value in number of cells (in this case equal to 5).
+{{ :tutorial:advanced_22.jpg |}}
+As a result, deforestation will cease in local regions as they reach a saturation threshold and move to new areas with lower probability of deforestation, simulating therefore the diffusion of deforestation.