Event-based rainfall warning regression model for landslide and debris flow issuing

Debris flow and landslide warnings are currently based on real-time monitoring of rainfall according to predefined warning lines. Conventionally, the rainfall variables combinations cumulative rainfall–duration ( R e – D ) and mean rainfall intensity–cumulative rainfall ( I m – R e ) for setting rainfall thresholds are used separately for landslide warning. The variables used in the regression analysis are correlated and a physical relationship I m = R e / D is available. Two-dimensional warning lines lack spatial feature and may not sufficiently reflect the rainfall characteristics required to initiate debris flows. A technical procedure using 3D regression analysis of the rainfall parameters interaction analysis was proposed. The rainfall warning regression surface is set on the basis of rainfall variables such as average rainfall intensity, effective cumulative rainfall, and duration. Here, a three-parameter, paraboloid rainfall warning regression surface generated using the variables of I m , D , and R e to determine the rainfall characteristics necessary to initiate debris flows and landslides is proposed. The proposed rainfall warning regression model reflects the rainfall characterization using a 3D diagram than the conventional threshold line. The regression results are converted in a multiple I m – D rainfall warning regression diagram containing various R e quantities for issuing landslide and debris flow warnings. Results show that the types of rainfall required to initiate debris flows and landslides include high rainfall intensity within a short duration and high cumulative rainfall over a long duration; moreover, debris flows could be affected by postseismic effects. The regression surfaces vary for rainfall events associated with different typhoons, which suggest that the initiation of landslides and debris flows is affected by the event that causes rainfall. An inclined plane surface is commonly used for describing a rainfall-induced landslide and debris flow regression surface for issuing warnings. The regression surface has parabolic geometry in postseismic landslide areas. The interactions of rainfall parameters using a three-dimensional regression analysis were studied and it was applied to the case of a catastrophic landslide and debris flow at Xiaolin Village in Taiwan.