assignment 3: kernel density estimationassignment 3: kernel density estimation ... steinocher...

UE Spatial Statistics 17.05.2016 Lukas Götzlich

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Assignment 3: Kernel Density Estimation

Within the third assignment the task was to analyse the pattern of supermarket and population

distribution in the city of Salzburg. The goal of the analysis is to find locations where the supply

of supermarkets is too high and to locate areas where the demand is higher than the amount of

retail stores. To perform the analysis, ArcGIS was used as tool. The methodological approach

goes along the analysis of Leitner and Staufer-Steinocher (2001) in the city of Vienna. One

difference might be that for my analysis no subgroups of supermarkets were investigated. The

focus is only on the major supermarket chains. With the command “Select by Attributes” in

ArcMap the following supermarket chains were selected for the investigation:

- Billa (+ Billa Corso)

- Hofer

- Lidl

- Merkur

- Penny

- Spar (+ Eurospar and Interspar)

- Zielpunkt

The following figure presents the selected retail-stores and the study area, in this case the city

of Salzburg with its border. For running the tool of the Kernel Density Estimation, this area was

used as processing extent.


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Fig. 1 Selected supermarkets for the analysis within the border of the city of Salzburg


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After the selection of the study area and the content, the Kernel Density of the supermarkets

had to be estimated. This was done according to the project outline of Leitner and Staufer-

Steinocher (2001). A tool for performing the analysis is provided in ArcMap which is called

“Kernel Density”. For executing the tool I took the default values. The only parameter that has

to be changed is the search radius or bandwidth. In order to find an appropriate radius the tool

was processed severel times. This was done for a bandwidth of 500m, 750m, 1000m and

1250m. The results can be seen in the figures below.

By comparing the results we can see very dense clusters for the images of 500m and 750m

bandwidth. As such a bullseye effect is decreasing the purity of the data a lot these might not

be ideal values for the analysis. This is a lot better for a bandwidth of 1000m or 1250m.

Especially for a value of 1000m we still can figure out some clusters around the districts of

Parsch and Gnigl where we can find the biggest ones. Some smaller ones are around Aigen,

Maxglan and Salzburg Airport and tiny ones in Lehen and Liefering. For 1250m bands width

the clusters seem to be vanished. That is why the best bandwidth is 1000m.


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Fig.2/3 Kernel Density Estimation of the Supermarkets for 500m (left) and 750m (right) bandwidth


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Fig.4/5 Kernel Density Estimation of the Supermarkets for 1000m (left) and 1250m (right) bandwidth


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Next to the calculation of the Kernel Density for the supermarkets and choosing a suitable

bandwidth, the same analysis was performed for the population grid. But before doing that the

data had to be prepared.

Fig. 6 Population grid with centroids for Kernel Density Estimation with the city of Salzburg

Fig. 6 shows the study area with the population grid with a particular centroid for each cell. The

area of one raster cell is 1km². Within the centroids the number of population for every cell is

stored. According to this the density calculation is based on population per square kilometre.

The centroids were calculated with the “Feature to Point” tool in ArcMap.


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The next step was to perform the Kernel Density Estimation for the population data.

Fig. 7 Kernel Density Estimation for Population

The result of the analysis for population shows the largest cluster in Lehen, Liefering and the

central parts of the city. Some smaller ones can be located in the southern part of Salzburg, in

Parsch and Aigen.

For all these analysis the classification type equal interval was used.


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The last step of the investigation is the combination of the supermarket and the population

density. Here for the two datasets are divided with the tool “raster calculator”. The result shows

regions with an oversupply of supermarkets and regions that are equipped with to less

supermarkets.

Fig. 8 Supply of supermarkets vs. population density


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In the figure above we can see that the regions of Gnigl/Parsch, Aigen, Maxglan and Liefering

are offering too many supermarkets (red or orange areas), but that there are also regions in

Lehen and in the downtown of Salzburg where the density of supermarkets is too low (green

areas).

assignment 3: kernel density estimationassignment 3: kernel density estimation ... steinocher...

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