# A SAR-Based Index for Landscape Changes in African Savannas
## Materials and Methods
### Index of Landscape Variability  
Besides observing inter-annual changes, general conclusions about developments within an area can be derived best based on direct comparisons of conditions at the beginning and the end of the investigated time. However, this excludes two major points in change detection.  
Firstly, savanna ecosystems are subject of large biotic and abiotic variation at multiple spatiotemporal scales [106]. It is a key task of remote sensing to reveal these variations to an adequate degree [107]. Besides simply comparing the intensity of changes, information on the temporal variability of regions--or in other words, the sum of all changes along the investigated period--has to be communicated as well. Surely, some areas remain stable after the transition of one LULC class into another while others tend to underlie regular variations. Analyzing changes over multiple images, especially in a region at the border between two ecosystems, surely should include the aspect of resilience towards long-term exterior influences.  
Secondly, class-based measurements are always subject to smaller misclassifications, especially if the data source is challenging. It is still widely reported that classifications based on SAR data alone are outperformed by approaches using multispectral optical data [108; 109; 110]. Similarly, single misclassifications within a time-series can distort the results towards changes which did not happen. In addition to that, the dates of image acquisitions are highly sensitive towards seasonal variations. Even if all images were taken at the same date of the year, inter-annual shifts in phenology of even a few weeks could cause the erroneous detection of 'pseudo changes'.  
Consequently, a second indicator is needed which spatially allocates high temporal variation within the study area and simultaneously quantifies the number of smaller changes which might only be subject to seasonal shifts in phenology.  
We therefore decided to apply a post-classification change vector analysis. Vector-based approaches make use of a feature space consisting of spectral or classified information and the temporal dimension [111; 112]. In our case, the variable determining the value of each hexagon grid cell is its weighted sum of natural resources as described in the previous section. These values are then plotted against the temporal period which is analyzed as exemplified in Figure 5: In a first step, the length of the vector describing overall change (C\({}_{\text{o}}\)) is calculated based on the NR values of 2007 and 2017. As a second variable contributing to the variability of an area, the length of the change vectors between each chronological image pairs are summed up to create the sum of annual changes (C\({}_{\text{a}}\)). For reasons of normalization, a factor of 10 has been applied to NR values for the calculation of vector lengths (e.g., a NR decrease of 0.55 to 0.40 during one year leads to a \(x\)-distance of 1.5 instead of 0.15. This is done because the y-distance is 1 except for 2011-2015). The ratio of C\({}_{\text{o}}\) and C\({}_{\text{a}}\) is then calculated and describes the variability (v) of the corresponding hexagon cell throughout the observed period. If C\({}_{\text{o}}\) and C\({}_{\text{a}}\) are of same length, v gets the value of 1. The longer the vectors of annual changes in relation to the overall change, the higher is the calculated variability v which is therefore a dimensionless value between 0 and 7, as the sum of the maximum NR value of 1 for a period of seven investigated years. This information can then be included in the discussion of the results as an indicator of variability and instability of an area.