The final step in the aptitude model is to consolidate reclassified Distance outputs (Aptitude Maps) in relation to the Recreational Facilities, Distance in relation to the existing Schools, Slope and Land Use.<\/p>\n
To take into account that some goals are more important than others in the aptitude model, you can weigh the data sets. You will give a higher percentage of influence (weighting) to the more important data sets. If all the data sets are of equal importance, you can give the same weighting to all of them.<\/p>\n
In the example, you know, from the examination of the problem, that the first objective is to locate the school near recreational facilities, and the second is to set it far from existing schools. The following percentages of influence will be attributed to the aptitude maps. Values \u200b\u200bbetween brackets are the percentages divided by 100 to normalize the values. These are assigned to each aptitude map:<\/p>\n
- \n
- Distance to recreational facilities: 50%<\/li>\n
- Distance to schools: 25%<\/li>\n
- Slope: 12.5%<\/li>\n
- Land use type: 12.5%<\/li>\n<\/ul>\n
The Distance<\/em> vs. Recreational Facilities<\/em> Aptitude Card has an influence of 50% (.5) on the final result, and the Distance from Schools<\/em> map has an influence of 25% (.25). Slope<\/em> factors and land use types<\/em> both have an influence of 12.5% \u200b\u200b(0.125). As in the assignment of aptitude scales, the weights assignment is a subjective process that relies on the most important goals of your study.<\/p>\n
<\/p>\n
Weighting analysis<\/strong><\/p>\n
<\/p>\n
What you have just read seems logical, and even intelligent. Do not be offended if you’re a fan of weights, but let’s try to see a little under the surface.<\/p>\n
What does it mean to say this mathematical transformation of importance of a criterion using weight value?
\nAnd most importantly, remember that the recipient of the result will necessarily be a decision maker to whom we will provide a map to help him make his decision.
\nWe have fully understood that the distance from existing schools and recreation centres criteria are more important for the decision-maker than the type of terrain (slope and occupancy).
\nApplying these weights, we will (we believe) respect this reasoning of the decision maker.<\/p>\nSo, as an example is better than a long speech, let’s take both:<\/p>\n
1- A site that is excellent according to the three criteria: distance to schools (value = 10), distance to recreation centres (value = 10) and slope (value = 10), will have as cumulative result for the three criteria (criterion value multiplied by the weight):<\/p>\n
0.5 x 10 + 0.25 x 10 + 0.125 x 10 = 8.75<\/p>\n
if the land use is the best (agriculture = 10) we will have as final result<\/p>\n
8.75 + 1.25 = 10<\/p>\n
if the land occupation is the worst (constructed = 3) we will have as final result<\/p>\n
8.75 + (0.125 x 3) = 9.125<\/p>\n
Do you believe the decision-maker can decide between 9,125 and 10? To the point of realizing that the second choice involves major drawbacks? Do you think that it is obvious at first glance?<\/p>\n
So let’s take another even more obvious example:<\/p>\n
2- A site that is excellent according to the three criteria: distance to schools (value = 10), distance to recreation centres (value = 10) and land occupation (value = 10) will have the following cumulative result of the three criteria:<\/p>\n
0.5 x 10 + 0.25 x 10 + 0.125 x 10 = 8.75<\/p>\n
if the slope is 30 \u00b0 it will have a value of 7. The final result will be<\/p>\n
8.75 + (0.125 x 7) = 9.625<\/p>\n
There, one borders perfection.<\/p>\n
Therefore a slope of 30 \u00b0 corresponds to a slope percentage of 57% which is more than double the feasible limit for a construction project!<\/p>\n
How do you think such a proposal will be perceived by the decision maker?<\/p>\n
Then, while crossing the criteria we will exclude values \u200b\u200bfrom the Slope criterion, with the Restricted option of the weighted overlay. This will prevent proposing sites with slopes in excess of 30%. Then, the only acceptable values \u200b\u200bof the criterion will be \u00a0 10, 9 and 8, the others being excluded. And while all the other criteria being constant, between the best slope and the worst, the final result will vary only 0.25!!!<\/p>\n
Contribution of slope criterion to the total if slope = 10 -> 10 * 0.125 = 1.25<\/p>\n
Contribution of slope criterion to the total if slope = 8-> 8 * 0.125 = 1.00<\/p>\n
You can try to change the weights, as much as you want and, you will always find an inadequacy of the results with the human reasoning. Simply because we do not weight criteria in our heads. What mixes up is the fact that we give different importance to criteria together with the fact that we assign a different weight which is not a very good idea.<\/p>\n
We will come back later. Now, let’s finish the exercise with Spatial Analyst.<\/p>\n
<\/p>\n
Weighted overlap with Spatial Analyst<\/strong><\/p>\n
<\/p>\n
Steps<\/strong> \u00a0<\/strong> :<\/strong><\/p>\n
- \n
- Open the Weighted Overlay tool. (Spatial Analyst Tools -> Overlay -> Weighted Overlay)
![\"\"](\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2018\/07\/tut41-300x208.png?resize=300%2C208\")
<\/li>\n - Type 1, 10, and 1 in the From<\/em>, To,<\/em> and By<\/em> text boxes<\/em>. The default ranking scale extends from 1 to 9 for each step of 1. A scale from 1 \u00a0 to \u00a0 10 was used when reclassifying the data sets, before adding input rasters to the Weighted Overlay tool, so you must set the ranking scales from 1 \u00a0 to 10 for each step of 1. This means that you avoid having to update the scale values \u200b\u200bafter adding your input data sets.<\/li>\n
- Click on Apply<\/li>\n
- Add the SlopeReclass<\/em> layer to the Weighted Overlay<\/em><\/strong> tool .\n
- \n
- Click the Add Raster Line<\/em><\/strong><\/li>\n
- For the input Raster<\/em><\/strong> , select \u00a0 PenteReclass<\/em> in the drop-down list and leave the input field set to Value<\/em> .<\/li>\n
- Click OK<\/em><\/strong><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n
The raster is added to the weighted Overlay Table. The Field<\/em> column displays the values \u200b\u200bof the SlopeReclass<\/em> data . The Scale Value<\/em> column replicates the Field<\/em> column because the Evaluation Scale has been set to include the range of values \u200b\u200bfor each input raster. At this point, you can change the Scale Values<\/em> for each class, but for this entry the values \u200b\u200bhave already been properly weighted during the reclassification.
\nRepeat the previous step for each of the reclassified data sets: LanduseReclass<\/em>, DistSchoolsReclass,<\/em> and DistRecSitesReclass<\/em> .
\nFor the SlopeReclass<\/em> entry, in the Scale Value<\/em> column , click the cell that has the value 1.
\nClick the drop-down arrow, scroll down the view, and then click Restricted<\/em>.<\/p>\n![\"\"](\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2018\/07\/tut42-300x270.png?resize=300%2C270\")
<\/p>\nIn this way, whatever the values \u200b\u200bof the other layers, the \u00a0 resultant value will be 0.<\/p>\n
Repeat this for values \u200b\u200b2 and 3.<\/p>\n
For the LandUseReclass<\/em> layer, set the Scale Value<\/em> that represents Water<\/em> and Wetlands<\/em> (0) to Restricted<\/em><\/strong>.<\/p>\n
Then, you assign a percentage of influence to each raster, based on the importance (or weighting) of each in the final aptitude card.
\nIn the % Influence<\/em><\/strong> column, enter the percentages for each of the input rasters:<\/p>\nDistSchoolsReclass out of 25
\nDistRecSitesReclass out of 50
\nSlopeReclass out of 13
\nLandUseReclass out of 12<\/p>\n![\"\"](\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2018\/07\/tut43-300x277.png?resize=300%2C277\")
<\/p>\nClick OK to run the tool.<\/p>\n
The final result, our aptitude map, appears as follows:<\/p>\n
![\"\"](\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2018\/07\/tut44-300x203.png?resize=300%2C203\")
<\/p>\nThe blue areas are the excluded areas (from the weighted overlay Restricted command).<\/p>\n
Green areas are the most suitable areas.<\/p>\n
In the next article we will perform these operations using the flexible aggregation command, applying fuzzy logic instead of the weights used in Spatial Analyst.<\/p>\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
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- For the input Raster<\/em><\/strong> , select \u00a0 PenteReclass<\/em> in the drop-down list and leave the input field set to Value<\/em> .<\/li>\n
- Open the Weighted Overlay tool. (Spatial Analyst Tools -> Overlay -> Weighted Overlay)