Gaussian-distribution-based hyetographs and their relationships with debris flow initiation

Although sophisticated models for predicting spatial and temporal rainstorm patterns have been proposed in past decades, the temporal patterns of extreme rainstorm events are still unknown, and the performance of natural and man-made slopes and debris flow mitigation measures have never been assessed from the viewpoint of temporal rainfall patterns. To this end, three methods were used to simulate the hyetograph of an extreme rainstorm, namely, typhoon Morakot, which resulted in a maximum rainfall of 2884mm in Taiwan from August 6-11, 2009. It was found that Gaussian-based hyetographs better simulated the rainstorm patterns recorded in the study area than conventional triangular and instantaneous intensity methods. Based on a satellite image investigation, a total of 32 events of reported debris flow disasters were identified with accurate times of debris flow strike and clear causative source slope failures adjacent to the disaster sites. Fundamental statistical parameters, namely the simulated time of peak rainfall intensity, t_p, and the standard deviation of rainfall duration, σ_t, were used to correlate the time of debris flow initiation. It was found that 94% (30 out of 32 events) of the investigated debris flows occurred between t_p-0.5σ_t and t_p+1.0σ_t, suggesting that intensive slope failures and debris flows occurred around the peak of hourly rainfall, associated with the steepest segment of the mass curve. It was also found that sites with larger source slope failure areas tended to have a longer delay between the time of peak hourly rainfall and the occurrence of debris flow. Results of the analyses revealed the potential of improving the accuracy of debris flow predictions using the proposed hyetograph method.