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tutorial:calculating_accumulated_cost_surface_and_least-cost_pathway [2013/07/27 20:55] juliana |
tutorial:calculating_accumulated_cost_surface_and_least-cost_pathway [2017/01/25 18:35] francisco [What will you learn?] |
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* How to calculate a friction surface, cost surface and least-cost pathway | * How to calculate a friction surface, cost surface and least-cost pathway | ||
- | * Functors: \\ - [[:calc_cost_map|Calc Cost map]]\\ - [[:calc_pathway_map|Calc Pathway map]] | + | * Functors: \\ - //[[:Calc Cost Map]]//\\ - //[[:Calc Pathway Map]]// |
This exercise requires the calculation of a friction surface, representing the relative cost of crossing a unit cell depending on the land use. We can express this surface both in terms of distance – no differential cost exits among types of land uses; hence the least-cost pathway will be the shortest route, i.e. the Euclidian distance – time, financial cost or some type of effort. Thus, this value is calculated in relation to some unit (time, transportation cost, etc). | This exercise requires the calculation of a friction surface, representing the relative cost of crossing a unit cell depending on the land use. We can express this surface both in terms of distance – no differential cost exits among types of land uses; hence the least-cost pathway will be the shortest route, i.e. the Euclidian distance – time, financial cost or some type of effort. Thus, this value is calculated in relation to some unit (time, transportation cost, etc). | ||
- | In this exercise, we explore the use of the functors [[:calc_cost_map|Calc Cost Map]] and [[:calc_pathway_map|Calc Pathway Map]]. To find an optimum solution for the accumulated cost surface, the functor //Calc Cost Map// uses a heuristic algorithm that recursively brushes a map until the best cost surface is obtained. As the number of passes increase so does an approximation of an optimum solution. Use “0” for an optimum solution, but in general, only two passes are sufficient to obtain a surface very close to the optimum solution. | + | In this exercise, we explore the use of the functors //[[:Calc Cost Map]]// and //[[:Calc Pathway Map]]//. To find an optimum solution for the accumulated cost surface, the functor //[[:Calc Cost Map]]// uses a heuristic algorithm that recursively brushes a map until the best cost surface is obtained. As the number of passes increase so does an approximation of an optimum solution. Use “0” for an optimum solution, but in general, only two passes are sufficient to obtain a surface very close to the optimum solution. |
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- | Open Dinamica EGO and load the aforementioned maps from lesson4\originals on the Map Viewer using the color table “mt”. Open the slope map using “Pseudocolor” as the current color palette and in the Histogram click on Limits to Actual and Histogram Equalize. As a first step, you need to reclassify the land use map to depict the cost of crossing each one of its land uses. Also you need to reclassify the slope map and then combine it with the land use map. | + | Open Dinamica EGO and load the aforementioned maps from ''lesson4\originals'' on the Map Viewer using the color table “mt”. Open the slope map using “Pseudocolor” as the current color palette and in the Histogram click on Limits to Actual and Histogram Equalize. As a first step, you need to reclassify the land use map to depict the cost of crossing each one of its land uses. Also you need to reclassify the slope map and then combine it with the land use map. |
For the land use map use the following table: | For the land use map use the following table: | ||
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| > 20 | 5 | | | > 20 | 5 | | ||
- | Let’s begin the model by loading the maps “landuse.tif” and “slope.tif” using the functor //Load Map//. Then, let’s incorporate the two previous tables. Add a Lookup Table from Table tab. | + | Let’s begin the model by loading the maps ''landuse.tif'' and ''slope.tif'' using the functor //[[:Load Map]]//. Then, let’s incorporate the two previous tables. Add a [[:Lookup Table]] from Lookup Table tab. |
You should have something like this:\\ | You should have something like this:\\ | ||
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- | Now place three //Calculate Map// and four //Number Map// functors, one within each //Calculate Map// and two //Number Map// functors within the third, and one //Number Table// within one of the two first //Calculate Map// functors and //Save Map//. Open //Number Map//, assign a unique number (1 and 2) to each one and assign “1” to //Number Table//. Finally connect Map “landuse.tif” to //Number Map// 1 and Map “slope.tif” to //Number Map// 2 of the two first //Calculate Map//. Then, connect the two first to the third //Calculate Map// and it to //Save Map//. Open //Save Map// and enter “friction.tif”. This is what you get. | + | Now place three //[[:Calculate Map]]// and four //[[:Number Map]]// functors, one within each //[[:Calculate Map]]// and two //[[:Number Map]]// functors within the third, and one //[[:Number Table]]// within one of the two first //[[:Calculate Map]]// functors and //[[:Save Map]]//. Open //[[:Number Map]]//, assign a unique number (1 and 2) to each one and assign "1" to //[[:Number Table]]//. Finally connect Map ''landuse.tif'' and Map ''slope.tif'' to //[[:Number Map]]// 1 of the two first //[[:Calculate Map]]//. Then, connect the two first to the third //[[:Calculate Map]]// respectively and it to //[[:Save Map]]//. Open //[[:Save Map]]// and enter ''friction.tif''. This is what you get. |
{{ :tutorial:cost3.jpg |}} | {{ :tutorial:cost3.jpg |}} | ||
- | Now, you need to enter the land use table in the functor //Lookup Table//. Open it with Edit Functor and start adding **keys** and **values** (fill in the fields and press the plus button).Open the //Calculate Map// that contains the //Number Table// and write the following formula: **t1[i1]**\\ | + | Now, you need to enter the land use table in the functor //[[:Lookup Table]]//. Open it with Edit Functor and start adding **keys** and **values** (fill in the fields and press the plus button). Open the //[[:Calculate Map]]// that contains the //[[:Number Table]]// and write the following formula: **t1[i1]**\\ |
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This formula will get the value from the map and use it as a key to access the table, therefore reclassifying the map according to the cost values.\\ | This formula will get the value from the map and use it as a key to access the table, therefore reclassifying the map according to the cost values.\\ | ||
\\ | \\ | ||
- | Enter the following equation into the second //Calculate Map//:\\ | + | Enter the following equation into the second //[[:Calculate Map]]//:\\ |
\\ | \\ | ||
**if i1 < 1 then 1 else if i1 < 5 then 1.3 else if i1 < 10 then 1.5 else if i1 < 15 then 1.9 else if i1 < 20 then 2.5 else 5**\\ | **if i1 < 1 then 1 else if i1 < 5 then 1.3 else if i1 < 10 then 1.5 else if i1 < 15 then 1.9 else if i1 < 20 then 2.5 else 5**\\ | ||
This corresponds to the slope friction table.\\ | This corresponds to the slope friction table.\\ | ||
\\ | \\ | ||
- | In the third //Calculate Map// enter:\\ | + | In the third //[[:Calculate Map]]// enter:\\ |
**i1*i2**\\ | **i1*i2**\\ | ||
\\ | \\ | ||
- | Save the model as “my_friction”, verify its integrity and if it is O.K., run it.\\ | + | Save the model as ''my_friction'', and run it.\\ |
\\ | \\ | ||
- | Open on the Map Viewer “friction.tif”, using “Pseudocolor” as Current Color Palette and in the Histogram click on Limits to Actual and Histogram Equalize. | + | Open on the Map Viewer ''friction.tif'', using “Pseudocolor” as Current Color Palette and in the Histogram click on Limits to Actual and Histogram Equalize. |
What do you see? Observe the red color representing the areas with high costs to cross. | What do you see? Observe the red color representing the areas with high costs to cross. | ||
- | {{ :tutorial:cost6.jpg |}} | + | {{ :tutorial:cost6.1.jpg |}} |
<note>You may feel free to use other software to view the maps.</note> | <note>You may feel free to use other software to view the maps.</note> | ||
- | + | Let’s move on to the second part of this exercise. Load ''town1.tif'' from ''\originals'' using //[[:Load Map]]// and ''railroad.tif'' using //[[:Load Categorical Map]]//. Remember that this functor categorizes a map.\\ | |
- | + | Drag //[[:Calc Cost Map]]// and //[[:Calc Pathway Map]]// from the Map Algebra tab and //[[:Save Map]]//. | |
- | Let’s move on to the second part of this exercise. Load “town1.tif” from \originals using //Load Map// and “railroad.tif” using //Load Categorical Map//. Remember that this functor categorizes a map.\\ | + | |
- | Drag //Calc Cost Map// and //Calc Pathway Map// from the Map Algebra tab and //Save Map//. | + | |
<WRAP center round info 60%> | <WRAP center round info 60%> | ||
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</WRAP>\\ | </WRAP>\\ | ||
+ | The **Source** port of [[:Calc Cost Map]] functor will receive the Map ''railroad.tif'' and the **Friction** port will receive the map output by the third Calculate Map //[[:Calculate Map]]//. Turn on **Diagonals Cost More**. This will penalize the movement across diagonal cells. Set **Maximum Number of Passes** to “2”. Leave all other options untouched. | ||
+ | Open //[[:Calc Pathway Map]]// now with the Edit Functor Ports. | ||
- | The **Source** port will receive the Map “railroad.tif” and the friction map output by the third //Calculate Map//. Turn on **Diagonals Cost More**. This will penalize the movement across diagonal cells. Set **Maximum Number of Passes** to “2”. Leave all other options untouched.{{ :tutorial:cost7.2.jpg |}} | + | Link Map ''town1.tif'' to the **Source** port <note tip>**TIP**: **Source**, in this case, also represents the destiny since the cost map was built from the existing railroad. Thus, this algorithm will search for the least-cost pathway from the source to the existing feature, i.e. the railroad.</note> |
- | + | Link the map output from //[[:Calc Cost Map]]// to the port **Cost** and Map ''railroad.tif'' to **Network** (because it represents a linear feature network) and the output **Network** port to //[[:Save Map]]//. {{ :tutorial:cost8.2.jpg |}} | |
- | + | ||
- | Open //Calc Pathway Map// now with the Edit Functor Ports. Link Map “town1.tif” to the **Source** port <note tip>**TIP**: **Source**, in this case, also represents the destiny since the cost map was built from the existing railroad. Thus, this algorithm will search for the least-cost pathway from the source to the existing feature, i.e. the railroad.</note> | + | |
- | + | ||
- | Link the map output from //Calc Cost Map// to the port **Cost** and Map railroad.tif to **Network** (because it represents a linear feature network) and the output **Network** port to //Save Map//. {{ :tutorial:cost8.2.jpg |}} | + | |
Activate the option **Use Lottery** (this is an artifact that permits the model to solve the path when two or more local minima are found).\\ | Activate the option **Use Lottery** (this is an artifact that permits the model to solve the path when two or more local minima are found).\\ | ||
\\ | \\ | ||
- | {{ :tutorial:cost9.jpg?300|}}//Calc Pathway Map// ignores cells with values equal or lesser than 0 or null cells. In turn //Calc Cost Map// needs a network map with null cells representing non-features. Go to Categorical Map and open it with the Edit Functor. Press the flag **Define Null Value** and make sure **Null Value** is set to “0”.\\ | + | {{ :tutorial:cost9.jpg?300|}}//[[:Calc Pathway Map]]// ignores cells with values equal or lesser than 0 or null cells. In turn //[[:Calc Cost Map]]// needs a network map with null cells representing non-features. Go to //[[:Load Categorical Map]]// and open it with the Edit Functor. Press the flag **Null Value** and make sure **Use specific value** is set to “0”.\\ |
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- | Click on //Save Map// with the Edit Functor, change the folder to an upper level, change the file format to “geotiff” and set **Suffix to Digits** to “0”, finally enter “railway.tif”. The final model will look as follows: {{ :tutorial:cost10.jpg |}} | + | Click on //[[:Save Map]]// with the Edit Functor, change the folder to an upper level, change the file format to “geotiff” and set **Suffix to Digits** to “0”, finally enter ''railway.tif''. The final model will look as follows: {{ :tutorial:cost10.jpg |}} |
- | Save the model to a new file “my_pathway.xml”, verify it and if it is O.K., run it. This is going to take only a little while. Dinamica EGO has superior performance in relation to most commercial GIS packages; you may want to try this model on other software just for performance comparison. Open on the Map viewer “railway.tif”, using “PseudoColor” as **Current Color Palette**. What do you see?\\ | + | Save the model to a new file ''my_pathway.egoml'', and run it (the model does not run on Dinamica 4, because it is been used two 'different' projections to calculate cost map). This is going to take only a little while. Dinamica EGO has superior performance in relation to most commercial GIS packages; you may want to try this model on other software just for performance comparison. Open on the Map viewer ''railway.tif'', using "PseudoColor" as **Current Color Palette**. What do you see?\\ |
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{{ :tutorial:cost11.2.jpg |}}\\ | {{ :tutorial:cost11.2.jpg |}}\\ | ||
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- | You may try to maximize the solution for the Calc Cost Map algorithm by setting the **Maximum Number of Passes** to “0”. Compare the time spent by this run and its resulting path with that of previous model? Did it make a big difference?\\ | + | You may try to maximize the solution for the //[[:Calc Cost Map]]// algorithm by setting the **Maximum Number of Passes** to “0”. Compare the time spent by this run and its resulting path with that of previous model? Did it make a big difference?\\ |
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- | This type of model can also be modified to develop simultaneously multiple paths. Open the model “join_towns.xml” in lesson 4 folder.{{ :tutorial:cost12.jpg |}} | + | This type of model can also be modified to develop simultaneously multiple paths. Open the model ''join_towns.egoml'' in lesson 4 folder.{{ :tutorial:cost12.jpg |}} |
- | This model shows how you can use //Calculate Map// to merge information from several maps into a single one. The product will be a map depicting the center cells for four towns. TIP: use always a sole cell to represent a location to be reached by //Calc Pathway Map//.\\ | + | This model shows how you can use //[[:Calculate Map]]// to merge information from several maps into a single one. The product will be a map depicting the center cells for four towns. TIP: use always a sole cell to represent a location to be reached by //[[:Calc Pathway Map]]//.\\ |
- | Now replace the input in Map “town1.tif” with the file “multiple_towns.tif” and change the file in Map “railway.tif” to “xrailways.tif”.\\ | + | Now replace, into model my_pathway.egoml, the input in Map ''town1.tif'' with the file ''multiple_towns.tif'' and change the file in Map ''railway.tif'' to ''xrailways.tif''.\\ |
Did you get something like this?\\ | Did you get something like this?\\ | ||
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{{ :tutorial:cost13.2.jpg |}}\\ | {{ :tutorial:cost13.2.jpg |}}\\ | ||
\\ | \\ | ||
- | If you go to Examples\run_lucc_northern_mato_grosso\run_roads_with_comments and open the model “mato_grosso_road.xml”, you will see how this set of algorithms can be adapted and combined to build a Road Constructor Module, a submodel that simulates the expansion of the road network in an Amazonian frontier region. This model is an example of the ability of Dinamica EGO platform for the ingenious design of spatial models. | + | If you go to ''Examples\run_lucc_northern_mato_grosso\run_roads_with_comments'' and open the model ''mato_grosso_road.egoml'', you will see how this set of algorithms can be adapted and combined to build a Road Constructor Module, a submodel that simulates the expansion of the road network in an Amazonian frontier region. This model is an example of the ability of Dinamica EGO platform for the ingenious design of spatial models. |
+ | [[tutorial:multiple_criteria_evaluation_in_dinamica_ego|Next Lesson]] | ||