Since shape metrics emerged in the landscape ecology as a new tool for quantitative evaluation of a landscape, it has become easier for geocomputation methods in GIS to adopt theirs principles. Nevertheless, there are still different scientific opinions about the usefulness of shape metrics. The paper describes shape metrics application for Corine Land Cover 1990, 2000 and 2006 areas (CLC) analysis along with statistical methods and discusses its benefits and disadvantages. The main goal of the paper is to evaluate CLC dataset without including attribute or qualitative information into analysis using shape metrics calculation. Thus, only geometric part of the data has been processed. Twenty eight metrics have been used for more than 900 areas (patches) from CLC dataset covering Olomouc region. Metrics values have been calculated and consequently used for correlation analysis, principal component analysis and cluster analysis. The results of the study represent complex evaluation of CLC Level 1 classes using, fundamentally, only the shape of CLC areas (patches). The analysis results show that shape metrics are very useful to identify groups of landscape patches with similar shape.
Since landscape ecologists can use capabilities of computer calculations, they are
able to apply numerous tools to quantify landscape patches in an effective way. For
this purpose, various indexes and metrics based on a patch shape have been derived,
because according to [
Shape metrics are exactly those methods used for quantitative description of a
patch shape, which represents real world objects. Shape and spatial metrics was
recently used in various topics, e.g. city footprint and form evaluation ([
There are several approaches how to classify landscape patches, but none of these are using shape metrics in combination with multivariate statistics for complex quantitative description of a landscape. It is common to use only a limited number of metrics to evaluate one specific patch group (e.g. habitats of particular species, humid areas, urbanized areas etc.). It is important to note that appropriate use of chosen metric depends on what is under the scope of study. One metric is more suitable for a one type of analysis, another for a different type. Although the use of metrics is purpose-dependent, metrics for this paper were chosen with an intention to calculate the most available ones for consequent multivariate statistics and tested if they can be (altogether) a tool for semi-automatic landscape classification. Similarly, analyzed patches used in this paper cover every patch type defined in CLC Level 1 classification nomenclature.
Thus, the approach presented in this paper is quite unique and the aim is complex landscape analysis via geocomputational methods to evaluate their usability for a landscape classification. Classification and proposed clustering methods were done with the view of the fact that only landscape patch shapes (geometry) were evaluated. Resulting clusters refer about the similarity of patch shapes and group areas with similar geometry. It is then evaluated what is the ratio of CLC Level 1 patches within clusters created only with the respect of shape metrics.
Analysis was performed on freely available CLC dataset from 1990, 2000 and
2006 using Level 1 nomenclature, which classifies a land cover into 5 main categories
− artificial surfaces, agricultural areas, forest and semi-natural areas, wetlands and
water bodies. Overall, for 944 landscape patches (sum from all years) from Level 1
shape metrics calculations were done. Landscape patches are elementary, further
nondivisive units of a landscape and according to [
Olomouc region (Fig. 1) was chosen as a study area, with more than 300 patches of
CLC nomenclature types in each reference year, in order to follow previous fractal
analysis of this area [
Shape metrics are fundamentally based on an area of a shape and its perimeter (these two characteristics are itself considered as shape metrics and are very easy to obtain), but most of metrics are more complicated to calculate and are treated as shape indexes. Anyway, there are plenty of software tools to perform metrics calculation. In this study, FRAGSTATS 4.1 and Shape Metrics toolbox for ArcGIS 10.x for Desktop was used. Multivariate statistics was performed in RStudio environment using R Project programming language.
List of metrics calculated in this study are in Table 1 and their description is
available in [
Prior to the shape metrics computing, their selection needed to be done, because calculation of some metrics is time-consuming − Shape Metrics toolbox requires vector data and since vertexes are necessary for complicated formulas of some metrics, calculation time for one single patch takes more than 10 minutes − and therefore those were excluded from the analysis.
Area index Circumscribing index Contiguity index Core index Core Area Index Number of Core Areas Dispersion index Normalized Dispersion index Depth index Normalized Depth index Detour index Normalized Detour index Exchange index Normalized Exchanged index
Girth index Normalized Girth index Gyrate index Perimeter-area ratio index Perimeter index (FRAGSTATS 4.1) Perimeter index (Shape Metrics Toolbox) Normalized Perimeter index (Shape Metrics Toolbox) Proximity index Normalized Proximity index Range index Normalized Range index Shape index Spin index
Normalized Spin index
Shape metrics in Table 1 were calculated for every single patch in CLC datasets. Next step was to perform Principal Component Analysis (PCA) of shape metrics to substitute the informational rich complete list and set main three components for consequent clustering. These components are in sum carrying 92 % of the original dataset variability and are composed of various metrics (main variance contribution from Gyrate index, Shape index, Core index, Normalized Core index, Proximity index, Exchange index, Spin index, Girth index, Dispersion index, Range index and Detour index). These and other metrics are forming the first, second and third component with different weights. Principal Component Analysis and the estimation of number of clusters could be depicted via graph of similarity of components within various numbers of clusters (Fig. 2).
Figure 2 shows a similarity, based on properties of shape metrics, in given number of clusters according to the method of least squares. It is clear that the similarity within 5 clusters is the highest with the respect of cluster number minimalization. The similarity highly increases between 4 and 5 numbers of clusters and does not significantly increase further. Therefore, it is optimal to cluster the dataset into 5 groups which correspond with the CLC Level 1 nomenclature.
Next step was to perform a cluster analysis. To find the best cluster method, a cluster simulation was run. Overall, 840 combinations of methods and individual settings combinations were given. It is quite subjective phase which cluster method and its settings to chose. It depends on what the user desires to achieve. Nevertheless, the simulation of cluster method suitability was performed using silhouette index. The higher the silhouette index the more suitable a clustering method is. There were only marginal differences among silhouette index values of the best proposed methods and that is why the selection of methods was partly left on researcher subjectivity.
Because there are five categories in CLC Level 1 nomenclature and according to withiness of clusters (Fig. 2), only those cluster methods with highest rank in simulation that define five groups were selected.
The first one was hierarchical method (method which creates tree structure −
dendrogram) called DIANA − DIvisive ANAlysis Clustering. The DIANA-algorithm
constructs a hierarchy of clusters; starting with one large cluster containing all objects
and then the cluster is divided until each cluster contains only a single object [
The second method was non-hierarchical, and partitioning, respectively, which
means that dataset is broken up into desired number of groups using medoids
(representative objects of a dataset, whose average dissimilarity to all surrounding
objects is minimized) and is called PAM − Partitioning Around Medoids. This
method is similar to the K-means clustering, but K-means uses means or centroids to
cluster a dataset. The PAM is treated to be more robust than K-means because of
minimizing dissimilarity instead of Euclidean distances ([
Both clustering methods were performed upon shape metrics and their principal components, respectively. Cluster groups were set only according to quantitative values and only non-spatial attribute space of the dataset was performed. Resulting groups are interpreted according to their patch type membership and shape characteristic. Clustering merge patches with the respect of their shape but not directly according to the patch CLC Level 1 type as formerly proposed. Thus, clusters are formed mostly of geometrically similar patches that are, for the most cases, partially patch CLC Level 1 type-independent. Anyway, there are some groups with a significant ratio of one specific patch type category.
First clustering (DIANA) delimitates 5 main clusters (Table 2). Main patch type in the first cluster is agriculture areas (49 %). In the second and third one, main patch type is artificial surfaces (59 %) and (42 %), respectively. Other patch types are not so dominant.
The very same principle as in the previous case was used to CLC dataset using PAM method of clustering. Target clusters defined by PAM are in Table 3. It is evident from both Table 3 and Figure 6 that this non-hierarchichal method distributed patches into groups more equally (excluding cluster number 5).
Main patch type in the first and fourth cluster is artificial surfaces (43 %) and (52 %), respectively. In the second and third one, main patch type is agricultural areas (45 %) and (61 %), respectively. Other patch types are not so dominant.
Excepting the group number 1, which is characteristic by containing rather small patches and those narrowly elongated, rest of the groups are the mix of various patches. Forests and semi-natural areas that made up self group using previous DIANA method (group number 4) are now joined with agricultural areas (in DIANA method group number 5) represented in this case by group number 5. Group number 3 contains mainly individual small patches. Barring the group number 1, it is very difficult to find some common characteristics for each group calculated by PAM clustering method. Therefore, it is more suitable in this case to perform analysis of the landscape using DIANA clustering method. However, it depends on the purpose what clustering method to use. If one want to have a complex view onto a landscape, DIANA could be used. On the other hand, PAM identified and pinpointed patches that are narrowly elongated more clearly, thus PAM could serve as a clustering method for elongated patches searching.
Aim of this analysis and calculation was to use clustering methods in order to create distinctive groups of landscape patches. Assumption was that CLC Level 1 patch type is directly influenced by their shape metrics, and vice versa. Ideally, if one of these clustering methods creates same clusters as original types of patches (e.g. artificial surfaces will form their own cluster), it will be very reliable to use them in future automatic classification of any patches. But none of cluster groups in both clustering methods were typical by containing one specific group of patch type in significant amount to claim that e.g. artificial surfaces has very unique shape and thus they form a special group. It is possible to use fuzzy words (e.g. it is more or less “agricultural” cluster) for concluding evaluation statements. Thus, it is needed to analyze patches individually and to search for contexts in detailed level in CLC nomenclature. On the other hand, maybe if larger area would be studied (e.g. entire Czech Republic), the similarity within the cluster would be greater due to the total number of patches involved into shape metrics computation. In other words, proportion of different patch types would not affect final results that much.
Hereby presented procedure could be also modified in the way that input clustering variables will not be principal components, but values of shape metrics themselves. Or another clustering method will be used, regardless to the cluster precision simulation.
Although previously presented results could not provide very convincing results at the first sight, the opposite is true because of the combination of strictly statistical methods together with spatial (visual) evaluation allowed new possibilities of data analysis to arise and unhide clusters of similar areas with similar properties.
Nevertheless, by using above mentioned methods, it is possible to group CLC patches according to their shape similarity, which is useful in a landscape evaluation. Consequent interpretation should take into account the knowledge of shape metrics and the geographic region for which landscape patches are analyzed.
Acknowledgments. The article was created within the project CZ.1.07/2.3.00/20.0170 and CZ.1.07/2.4.00/31.0010, supported by the European Social Fund and the state budget of the Czech Republic.