A risk reduction program was developed after debris-flow disaster analysis is conducted using mitigation structures, evacuation measures and community restrained expansion strategy. The risk assessment method delineates hazard zones and analyzes vulnerability and the resilient capacity of an affected area, allowing the prediction of losses of properties and lives, and the corresponding risk. It can also be used to evaluate performance of a risk reduction program. The proposed method was applied to the Songhe community as a case study to assess debris-flow risk and performance of reduction programs consisting of mitigation structures, evacuation measures and a restrained expansion strategy. Total annual risk decreased to $0.01 million from $0.72 million for the No. 1 Torrent and to $0.36 million from $1.22 million for the No. 2 Torrent after mitigation structures were installed, and evacuation measures were implemented based on restrained expansion. Although mitigation structures are costly, they can reduce the size of hazard zones. Delimitating the Designated Soil and Water Conservation Area restrains community expansion and decreases possible losses. Although evacuation measures cannot reduce the size of hazard zones, they effectively increase the resilient capacity of residents. The benefit-cost ratio for mitigation structures exceeds 1.0 for both torrents with an average of 3.87; the benefit-cost ratio for evacuation measures is markedly greater than 1.0. Combining mitigation structures and evacuation measures increases the total benefit with a benefit-cost ratio of 4.38. Analytical results showed that the risk reduction program is cost-effective.

The prediction and advanced warning of landslide hazards in large-scale areas must deal with a large amount of uncertainty, therefore a growing number of studies are using stochastic models to analyze the probability of landslide occurrences. In this study, we used a modified Thiessen’s polygon method to divide the research area into several rain gauge control areas, and divided the control areas into slope units reflecting the topographic characteristics to enhance the spatial resolution of a landslide probability model. We used a 2000–2015 long-term landslide inventory, daily rainfall, and effective accumulated rainfall to estimate the rainfall threshold that can trigger landslides. We then employed a Poisson probability model and historical rainfall data from 1987 to 2016 to calculate the exceedance probability that rainfall events will exceed the threshold value. We calculated the number of landslides occurring from the events when rainfall exceeds the threshold value in the slope units to estimate the probability that a landslide will occur in this situation. Lastly, we employed the concept of conditional probability by multiplying this probability with the exceedance probability of rainfall events exceeding the threshold value, which yielded the probability that a landslide will occur in each slope unit for one year. The results indicated the slope units with high probability that at least one rainfall event will exceed the threshold value at the same time that one landslide will occur within any one year are largely located in the southwestern part of the Taipei Water Source Domain, and the highest probability is 0.26. These slope units are located in parts of the study area with relatively weak lithology, high elevations, and steep slopes. Compared with probability models based solely on landslide inventories, our proposed landslide probability model, combined with a long-term landslide inventory and rainfall factors, can avoid problems resulting from an incomplete landslide inventory, and can also be used to estimate landslide occurrence probability based on future potential changes in rainfall.

Landslide spatial, temporal, and size probabilities were used to perform a landslide hazard assessment in this study. Eleven intrinsic geomorphological, and two extrinsic rainfall factors were evaluated as landslide susceptibility related factors as they related to the success rate curves, landslide ratio plots, frequency distributions of landslide and non-landslide groups, as well as probability–probability plots. Data on landslides caused by Typhoon Aere in the Shihmen watershed were selected to train the susceptibility model. The landslide area probability, based on the power law relationship between the landslide area and a noncumulative number, was analyzed using the Pearson type 5 probability density function. The exceedance probabilities of rainfall with various recurrence intervals, including 2, 5, 10, 20, 50, 100 and 200 yr, were used to determine the temporal probabilities of the events. The study was conducted in the Shihmen watershed, which has an area of 760 km² and is one of the main water sources for northern Taiwan. The validation result of Typhoon Krosa demonstrated that this landslide hazard model could be used to predict the landslide probabilities. The results suggested that integration of spatial, area, and exceedance probabilities to estimate the annual probability of each slope unit is feasible. The advantage of this annual landslide probability model lies in its ability to estimate the annual landslide risk, instead of a scenario-based risk.