Weighted linear summation

Case study St. Gittal

The following paragraph examines weighted overlay using the example of the wolf habitat in St. Gittal in more depth. To gain a more realistic model of suitable habitats, the example no longer uses only binary input data as the Boolean overlay, but ratio data:

Vegetation density rather than "forest / non forest"
Slope rather than "steep / not steep"
Population density rather than "settlement / no settlement"

The simplest approach to a weighted overlay is the weighted linear summation in the raster model. The following steps show the standard approach to the application of this algorithm:

Selecting the criteria: the first step is to choose criteria that characterize the area you are looking for;
Standardization: the different measurement scales of the input data need to be matched. It does not make sense to calculate the percent slope directly with population density. Therefore, different units of a standardized numerical index scale (e.g. 0-1, 0-100, 0-255) are assigned to the input data. Consequently, the values of the resulting suitability layers will no longer have units but a numerical suitability index. Assigning input values to the index scale can be accomplished in different ways. The simplest is a linear assignment. With weighted overlay, the translation of heterogeneous input data into a uniform scale for all layers is called standardization.
Distribution of weights: each information layer receives a weight. The weight reflects the relative importance of the each layer respective to the other. The largest weight is assigned to the most important layer. The correct choice of weights is discussed in the section "Determining the weights".
Application of the algorithm: the algorithm of the weighted linear summation multiplies all grid cells of a layer by their weight. Then, the layers are added together. In the resulting suitability layer the suitable cells have high values while the not suitable cells have low values.

This animation provides you with the possibility to conduct a suitability analysis of your own for the community of St. Gittal. The task is to find potential habitat for the wolf. Decide how the input layers are standardized and weighted.

Gewichtete lineare Summation

Click to enlarge

Selecting the criteria: Selecting the criteria: as you have seen earlier, the wolf prefers dense vegetation and steep, rocky terrain. Now you can also take into consideration that he is likely to avoid settlement areas. The following information layers are available:
- Forest density (top row): 4 vegetation categories: bare (0%), little vegetation (40%), heavily vegetated (60%), and totally covered with vegetation (100%).
- Slope (middle row): 3 slope categories: low (10), medium (20), high (30).
- Population density (bottom row): 3 categories of population density: uninhabited (0), sparsely populated (100), and densely populated (200).
Standardization: all input grids should be converted to the value range from 0 to 1. Fill in the values 0 and 1 into the appropriate fields in the animation. Note that for some thematic layers you need to invert the range of values in addition to the standardization. This is the case when a high value of the input layer is unsuitable for the wolf. In that case, the value 0 needs to be assigned.
Distribution of weights: as an expert on wolves, you need to assign weights to each layer. Enter the weights into the fields shaped like weight-stones. The protective forest gets the greatest importance; the forest layer gets a weight of 5; the slope a weight of 3; and the uninhabited areas a weight of 2.
Application of the algorithmthe requested suitability layer is the result of multiplying the layers with their weights and the final summation of the layers. A click on the "calculate"-button delivers the results. The areas most suitable for the wolf (with the given assumptions) have values ranging from 7.5 to 8.5. Areas not suitable for the wolf show low values through to 0 (=totally unsuitable).

Now it is your turn to try other standardizations and weightings. Experiment with extreme weight distribution. Pay attention to the changes in the resulting suitability map and try to interpret the results.