# The Role of Earth Observation, with a Focus on SAR Interferometry, for Sinkhole Hazard Assessment
## 3 Statistical Modelling and Probabilistic Sinkhole Hazard Assessment  
It has been noted that valuable indications of an area's vulnerability to sinkhole and subsidence formation can be obtained from knowledge of past events [12; 13; 15; 31; 37]. The process of sinkhole hazard map generation generally involves the mapping of the regional parameters that may impact on collapse occurrences [31] and/or the analysis of the spatial distribution of past sinkholes [15]. A significant component in these processes involves the compilation of a sinkhole inventory for an area under investigation and the subsequent analysis of cause-and-effect relationships between sinkhole occurrences and local conditions [11; 12; 13; 14]. Various approaches to the compilation of sinkhole susceptibility maps have been described [15]. This includes (1) approaches based on the spatial distribution (density) of sinkholes, (2) heuristic models based on the presence of particular controlling factors and (3) probabilistic models that involves the analysis of statistical relationships between existing sinkholes and controlling conditions. Both heuristic models and sinkhole density approaches are geared towards the creation of sinkhole susceptibility maps [15], which aid in defining prevention and remediation measures [14]. In this way, the most hazardous areas can be avoided for further development. On the other hand, probabilistic models aims to analyse cause-and-effect relationships between sinkhole occurrences and local conditions [15], thereby providing valuable information for the compilation of sinkhole risk management plans to reduce dissolution processes. An understanding of the factors controlling sinkhole development is deemed necessary for the development of sinkhole probability models. In an attempt to develop sinkhole probability models for Minnesota, factors such as distance to nearest sinkhole, sinkhole density, bedrock geology and depth to bedrock were included in a decision tree model [38]. However, the models did not incorporate controlling factors. In contrast, a method for assessing sinkhole probability and hazard was tested for the Ebro Valley in Spain [37] which included an assessment of the contribution of specific variables controlling sinkhole development and their effect on the predictive capability of the models. The results were used to define sinkhole susceptibility models for sinkhole hazard map generation [37]. Further refinements to these models included the incorporation of magnitude and frequency relationships to estimate the probability of a certain area being affected by a sinkhole of a specific size [39]. Further examples of sinkhole risk assessments based on sinkhole inventories are  
Figure 3: A sinkhole, and associated tension cracks, that resulted in road closure in Gauteng, South Africa in 2018. The sinkhole is in the process of being rehabilitated and has been filled with concrete. (photo credit: Dilnaza Patel). available for several regions world-wide [12; 13; 14; 15; 17; 37]. In general, statistical investigations reveal that the probability of sinkhole development in undeveloped areas is statistically small when measured as a percentage of the land area [13]. However, the anthropogenic activities in highly developed, urbanised areas have accelerated the development of sinkholes [12; 13; 37]. In fact, in the dolomitic terrain in the densely populated Gauteng Province of South Africa for example, statistical analysis of sinkhole inventories revealed that between 94 % and 99 % of sinkholes were triggered by anthropogenic activities while only between 1% and 6% could be attributed to natural causes [13]. In particular, the development density of these areas were found to be a significant factor leading to the conclusion that higher densities of water bearing services were associated with higher likelihood of leaking services and, therefore, higher probabilities of sinkhole development [13]. The investigation also revealed a correlation between cumulative rainfall and sinkhole occurrences.