In this paper the concept of fuzzy overlay was used to delineate suitable habitats for alpine marmots in the Dachstein region in Upper Austria. Four criteria were chosen as important factors for possible habitats for marmots: grassland as preferred type of biotope, an elevation between 800 and the foot of the glacier, the mean annual sunshine duration as well as the distance to skiing areas. By applying fuzzy membership values from 0-1 and overlaying the derived raster, a map with continuous suitability values is obtained. For decision making and finding the optimal areas defuzzification as well as a sorting out concerning the size of the areas is necessary as a final step.
Fuzzy overlay analysis is an interesting approach concerning multi criteria overlay analysis. By using fuzzy sets instead of crisp boundaries, fuzzy logic allows partial membership and multiple membership. This makes it ideal to overcome uncertainties in data and in the definition of classes.
CONTENT
Abstract
1. INTRODUCTION
2. FUZZY OVERLAY APPROACH
3. EXAMPLES FOR THE USE OF FUZZY OVERLAY
4. STUDY AREA
5. ALPINE MARMOTS AND THEIR CRITERIAS FOR A SUITABLE HABITAT
6. DATASETS FOR THE ANALYSIS
7. DATA PREPARATION
8. FUZZY OVERLAY ANALYSIS
8.1. FUZZY MEMBERSHIP
8.2. FUZZY OVERLAY
8.3. DEFUZZIFICATION
9. RESULT AND CONCLUSION
REFERENCES
TABLE OF FIGURES
ABSTRACT
Fuzzy overlay analysis is an interesting approach concerning multi criteria overlay analysis. By using fuzzy sets instead of crisp boundaries, fuzzy logic allows partial membership and multiple membership. This makes it ideal to overcome uncertainties in data and in the definition of classes. In this case the concept of fuzzy overlay was used to delineate suitable habitats for alpine marmots in the Dachstein region in Upper Austria. Four criteria were chosen as important factors for possible habitats for marmots: grassland as preferred type of biotope, an elevation between 800 and the foot of the glacier, the mean annual sunshine duration as well as the distance to skiing areas. By applying fuzzy membership values from 0-1 and overlaying the derived raster, a map with continuous suitability values is obtained. For decision making and finding the optimal areas defuzzification as well as a sorting out concerning the size of the areas is necessary as a final step.
1. INTRODUCTION
The Bachl -Alm in the municipality of Filzmoos is well-frequented by hikers because it is famous for its trusting marmots around the hut. Moving a few kilometres to the north, across the Dachstein ridge into the federal state of Upper Austria, there are hardly any marmots. The environmental conditions should not differ that much from Bachl-Alm, where marmots were introduced by humans. So maybe this animal could also live in the northern area of Dachstein and enrich the fauna of Upper Austria. A typical approach in GIS to find suitable habitats for a certain species is multicriteria overlay analysis. Typically, one would think of the more common weighted or Boolean overlay but in this case another method is used: fuzzy overlay. The objective of this work is to get the potential range of marmots in the protected area of Dachstein by the use of fuzzy overlay analysis. Potential range is described as union of occupied (natural) and invadable area, which would be achieved if all dispersal constrains are overcome. (Booth 2013: 175/176) Within this potential range the best habitat for marmots should be extracted and displayed.
2. FUZZY OVERLAY APPROACH
The fuzzy overlay approach combines the principles of fuzzy logic, which was originally found in mathematics as a set theory, and traditional suitability and site selection analysis in GIS. In comparison to Boolean overlay where an entity is either part of a class or not, fuzzy overlay does not work with crisp boundaries and allows partial memberships. These fuzzy memberships are expressed with values from 0 to 1 to which the original values are transformed. They give information about the possibility whether the entity belongs or does not belong to the fuzzy set. 1 in this case means it is definitively a member of this class whereas 0 means the opposite. The values in-between indicate the likelihood of membership, the higher the value the higher the possibility of being a part. In addition to that fuzzy overlay also supports multiple memberships. (Weerasiri et al. 2014: 3), (Qiu et al. 2013: 171)
These properties of fuzzy overlay analysis lead to some advantages that weighted overlay and Boolean overlay do not share: Fuzzy membership allows to overcome uncertainties in the measured data as well as in the definition of classes. (Zabihi et al. 2017: 217) Data acquisition is not always 100 percent accurate and contains errors: This can be balanced by applying fuzzy sets. Furthermore, many phenomena show a degree of vagueness and cannot be perfectly fit into classes with crisp boundaries, especially when it comes to processes in nature. In weighted overlay the result changes strongly depend on to the given weights and the classes that are built. But it would not be “reasonable to assign an area with 1,499 mm of annual precipitation to the suitability rating of 1 while an area with 1,501 mm of annual precipitation is given a suitability rating of 2”. (Qiu et al. 2013: 170) In fuzzy overlay a factor below a formulated threshold is not excluded for being taken under account as suitable area. (Qiu et al. 2013: 171) Due to the conversion into uniform scales which makes them easier comparable. Also, individual information about the input layers does not get lost after the overlay compared to Boolean and weighted overlay. It provides more detail because of the partial degree of suitability across space (Alsamadisi 2016)/Qui et al 2013:180/181) Zabihi et al. (2017:216-217) describes fuzzy logic models as easy interpretable and communicable between stakeholders of a project. Fuzzy rules without crisp boundaries correspond better to human’s way of thinking and perception of the world. Results derived with fuzzy logic seem to be more informative to decision makers in contrast to the traditional overlay approaches and better support the implementation of improvements for further analysis. (Qiu et al. 2013: 171) In their analysis, Baidya et al. (2014:8-9) describes the results of a fuzzy overlay approach as more accurate and consistent compared to the results of the weighted overlay approach. Weighted overlay analysis tends to overestimate or underestimate potential sites much more.
3. EXAMPLES FOR THE USE OF FUZZY OVERLAY
Fuzzy overlay is already well recognized as a useful tool to determine suitable habitats for different species. Zabihi et al. 2017 used fuzzy logic in their analysis to find suitable nesting locations for sage grouses in Wyoming. Their work revealed the importance of the absence of human disturbance for successful nesting of this species. González-Tennant (2013) has proven this approach must not only be applied to really existing species but can also be used in scenarios. In his work he picked fuzzy overlay as best approach to predict suitable habitats for zombies based on his previous zombie outbreak analysis. Another application is the model of the distribution of invasive species like the kudzu (Qiu et al. 2013). The plant was former domestic in Japan but was brought to the US and spread there. They could proof that the fuzzy logic analysis provided pretty accurate results of the distribution of kudzu and was close to the actual distribution map of the plant. Fuzzy overlay does not necessarily involve the habitat of a species, it can be used for all kinds of suitability and site selection analysis. Baidya et al. (2014) try to highlight agricultural areas that could be used more efficiently through the change of the land use (intensive agriculture, horticulture, afforestation) in the East Khasi Hills District of Meghalaya in India. Finally, fuzzy overlay analysis could also be used to depict threats for human’s health and the environment. Weerasiri et al. (2014) investigated areas that are potentially contaminated with arsenic around iron mines. They describe fuzzy overlay as straightforward approach and useful for all kinds of heavy metals and polluted materials that are transported with water through soil.
4. STUDY AREA
As study area the „FFH- und Vogelschutzgebiet Dachstein" area was chosen, which is a protected area according to the Natura 2000 network and the standards of the European Union. It is located in southern Upper Austria on the border to Salzburg and Styria and belongs to three municipalities: Gosau, Hallstatt and Obertraun. With an extent of 14.630 hectares it is the second largest protected area after the Kalkalpen National Park. The protected area is characterised by the Dachstein Plateau with the Hoher Dachstein (2995) as highest mountain of Upper Austria and Styria. As part of the Northern Limestone Alps lime it is a strongly carstic region with lime as the dominant rock type. The Dachstein area is famous for its permanent glaciers which are the easternmost glaciers of the Alps and the only ones in Upper Austria. Apart from typical alpine biotopes the protected area offers also mixed forests at the lower northern slopes and alluvial forests around the Gosau Lakes in west (figure 1). Because of its wide variety it is a hotspot for tourism (hiking, skiing and caves) and offers infrastructure for this purpose even though it is a protected area. The choice for the Dachstein area as study area was made because of the good availability of data for the analysis. The government of Upper Austria offers various layers that could be useful for the analysis and even a shapefile with the protected areas of the state. Furthermore, the Dachstein region is the only region with high alpine character in Upper Austria and therefore the only possibly suitable region. (Land Oberösterreich n.d.)
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Figure 1 Dachstein area with lake Gosau (source: Wikipedia.com)
5. ALPINE MARMOTS AND THEIR CRITERIAS FOR A SUITABLE HABITAT
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Figure 2 Alpine marmots (source: www.deutschlands-natur.de)
With a length of 40-50 centimetres, the alpine marmots (Marmota marmota) (figure 2) is the second biggest rodent of Austria after the beaver. Marmots are often associated with mountains and used as a symbol for the Alps. Actually, marmots are denizens of the tundra and were widespread over Europe during the last ice age. With the retreat of the glaciers and the change from tundra to forest most of the original habitat of the marmot got lost. Alpine marmots’ todays occurrences in the Alps and the Tatra mountains correspond to their former habitats and are the last retreat areas in Europe. They are able to cope with extreme alpine conditions and can survive up to the foot of the glacier (occasionally up to 3000m). Their lowest border of vertical distribution is 800 meters, so there are no populations that undercut this mark even if the biotope would fit. This is due to the fact that marmots cannot handle warm temperatures very well, at 20 degrees Celsius they already suffer from heat stress. Even if they do not like warm temperatures, marmots prefer sunny slopes to hillsides that get less solar radiation. This has two reasons: First, the growing season of their favourite food (herbs and grass) is longer and serves them with better nutrition. Secondly, they like to take sunbaths to get rid of parasites. By lying flat on the ground fleas and lice get expelled with the help of UV radiation and the heating of the fur. (Arnold 1999)
Apart from parasites the most dangerous threats for marmots are the red fox, the golden eagle and the winter. To increase their survival rate, they live together in family groups up to 20 individuals. As highly social animals they warn each other with loud whistles when an enemy appears in their territory. On average a marmot family uses 2,5 hectares of space with the characteristic burrows, which they dig for protection against predators and hard weather conditions. Moreover, they are crucial to survive the winter through hibernation, so marmots are dependent on soil that is not too compact. Another factor is water permeability, the burrows should also not be flooded with water. Moraines and debris fulfil both of this condition and seem to be the optimal underground. (Arnold 1999)
By looking at marmots’ requirements for their environment and their daily life there are many factors that could be taken into account for this habitat analysis. Three criteria are essential and more important than others:
- Marmots do not live under 800 metres of altitude and above the vegetation limit. This factor can be covered with an elevation map.
- Marmots need herbs and grass to eat because this serves as their main nutrient source. This factor can be covered with a vegetation/biotope map.
- Marmots rely on burrows as protection against natural enemies and the harsh environment. This factor can be covered with a soil map.
In addition to this, the following factors were also regarded:
- Marmots favour sunny areas because of two above-mentioned reasons. On the one hand this could be solved with the aspect tool which calculates the slope direction. Southern-faced slopes would then have a higher suitability as northern or western faced slopes. On the other hand, a sunshine duration map could give us information about areas that obtain more solar radiation from the sun. In this case the decision was made in favour of the sunshine map, even if the resolution is coarser. For the purpose of this analysis the dataset is more precise because it treats the actual incoming sunlight and reliable because it covers a period of 30 years.
- Due to the fact that the study area is a protected area human influence is already reduced to a minimum. An exception is the skiing region Dachtein/Krippenstein which is located in the east of the study area. The usage of artificial snow extends the period were skiing is possible, but this happens at the expense of the vegetation period. Furthermore, the usage of heavy vehicles like snow groomers makes the soil more compact and therefore harder to dig. Finally, noise could potentially disturb them in their hibernation. To sum up, the delineated habitat should not be too close to the skiing area to avoid these negative effects.
6. DATASETS FOR THE ANALYSIS
The following table should provide an overview of the dataset that were used for further analysis. The layer on the pictures are all already clipped and prepared according to the description in the next chapter.
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Figure 3 Biotop Map
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Figure 4 Digital Elevation Map
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Source: Land Oberösterreich/ZAMG
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Figure 6 skiing area map
7. DATA PREPARATION
Before the actual analysis the data had to be prepared to fulfil the requested criteria and to be accessible for the ArcGIS Pro Tools. The biotope map was clipped to the extent of the Natura 2000 protected area Dachstein and the different polygons were merged after their biotope type names. For the purpose of this analysis it was not necessary to keep a differentiation between 24 types of natural environments and therefore categories of biotopes were built. For instance beech forests and spruce forests are both about the same level of suitability for marmots and are integrated into the new category “forest”. After the simplification of the dataset seven relevant biotope maps were left including: Forest, alpine grassland, rocks, water, mountain pine and other alpine biotopes, bog and permanent glacier.
Further they were transformed into a raster with the determined grid size for this project of 10x10 meters. The last step contains a reclassification of the values in such a way that they are already sorted according to their suitability from 0-10 (e.g. alpine grassland gets 10 whereas permanent glacier gets a value of 0). The digital elevation raster and the sunshine duration map were already in the raster format, so they only needed to be masked to the size of the study area. Additionally, the sunshine raster needed to be set to the same resolution as the other layers. Finally, it was important to derive a raster from the skiing slope polygon which also gives information about the distance to the slope. This task was done with the Euclidian distance tool which combines these two steps.
8. FUZZY OVERLAY ANALYSIS
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Figure 7 Fuzzy overlay workflow (source: Qiu et al. 2014)
Figure 7 shows a typical workflow of a fuzzy overlay analysis for delineating suitable areas. First the values of the environment factors, in this case the already prepared biotope, elevation, sunshine and skiing layer, are fuzzified. This is done by applying fuzzy membership values from one to zero and as a result one gets a new raster for each factor. In the next step the overlay happens and the result is a merged raster with values that give information of suitability for each pixel. Subsequently, a defuzzification is usually done for decision making and getting the areas that match the criteria best. In the next chapters these steps are explained in more detail and it is shown how this is applied to the data that was used.
8.1. FUZZY MEMBERSHIP
This step involves the transformation of the initial values into a common scale from one to zero. ArcGIS Pro offers seven different types for performing fuzzy membership: (ESRI n.d. a) Fuzzy Gaussian The values are displayed as a normal distribution with a midpoint which gets the value 1. The midpoint represents the optimal case concerning suitability, upper and lower values are assigned with decreasing membership values. At a certain distance to the midpoint values are definitely not a member of the fuzzy set and get therefore the value zero. In addition to the midpoint it is possible to define a spread value which determines the size of the transition zone between one and zero. The higher the spread parameter, the faster the membership values decrease to zero.
Fuzzy Large
Again, a midpoint is defined but it defines the crossover point. This means that values that are larger have a greater possibility to be member of the fuzzy set than values below.
Fuzzy Small
Fuzzy Small is the opposite of Fuzzy Large, here values below the midpoint have a higher likelihood of being member of the set.
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