Linear discriminant analysis to describe the relationship between rainfall and landslides in Bogota, Colombia

Bogota is located in the central Andean region of Colombia, which is frequently affected by landslide processes. These processes are mostly triggered during the rainy season in the city. This fact remarks the importance of determining what rain-derived parameters (e.g. intensity, antecedent rain, daily rain) are better related with the occurrence of landslides. For this purpose, the linear discriminant analysis (LDA), a technique derived from multivariate statistics, was used. The application of this type of analysis led to obtain simple mathematical functions that represent the probability of occurrence of landslides in Bogota. The functions also allow to identify the most relevant variables derived from records of rainfall linked to the generation of landslides. A proof of concept using the proposed methodology was done using historic rainfall data from a 9-km(2) area of homogenous climatology and geomorphology in the south part of Bogota. Landslides needed to be grouped for the LDA. Each one of these grouping categories represents landslides that occurred in similar geomorphologic conditions. Another set of events with no landslides was generated synthetically. Results of the proof of concept show that rainfall parameters such as normalized rainfall intensity IMAP, normalized daily rainfall RMAP and rainy-days normal RDN have the best statistical correlation with the landslides observed in the zone of analysis.