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tutorial:using_local_saturation [2013/07/24 15:29]
juliana
tutorial:using_local_saturation [2020/02/18 23:12] (current)
argemiro
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-Load the model simulate_deforestation_using_local_saturation.xml” ​from \Examples\advanced\local_saturation +Load the model ''​simulate_deforestation_using_local_saturation.egoml'' ​from ''​\Guidebook_Dinamica_5\Models\additional_resources_lucc\local_saturation''​. ​Local saturation prevents a change from occurring within a specific region, in which a class area is greater than an established threshold (Fig.1). 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:
-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\\ +**P<​sub>​2</​sub> ​P<​sub>​1</​sub> ​* (Li – Oc) / (Li + Oc), case Li >= Oc\\ 
-P2 = 0, case Li < Oc+P<​sub>​2</​sub> ​= 0, case Li < Oc
 ** **
  
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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: ​ 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\\ +**P<​sub>​2</​sub> ​P<​sub>​1</​sub> ​* (5 - Oc) / (5 + Oc),  case Li >= Oc\\ 
-P2 = 0, case 5 < Oc**+P<​sub>​2</​sub> ​= 0, case 5 < Oc**
  
  
-[{{ :​tutorial:​advanced_21.jpg |Two landscapes without and with local saturation effect}}]+[{{ :​tutorial:​advanced_21.jpg |Fig.1 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: ​+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)** **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:+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** **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. ​
 +
 +[[tutorial:​landscape_metrics_in_dinamica_ego| Next Lesson]]