Objective definition of rainfall intensity–duration thresholds for the initiation of post-fire debris flows in southern California

Abstract

Rainfall intensity–duration (ID) thresholds are commonly used to predict the temporal occurrence of debris flows and shallow landslides. Typically, thresholds are subjectively defined as the upper limit of peak rainstorm intensities that do not produce debris flows and landslides, or as the lower limit of peak rainstorm intensities that initiate debris flows and landslides. In addition, peak rainstorm intensities are often used to define thresholds, as data regarding the precise timing of debris flows and associated rainfall intensities are usually not available, and rainfall characteristics are often estimated from distant gauging locations. Here, we attempt to improve the performance of existing threshold-based predictions of post-fire debris-flow occurrence by utilizing data on the precise timing of debris flows relative to rainfall intensity, and develop an objective method to define the threshold intensities. We objectively defined the thresholds by maximizing the number of correct predictions of debris flow occurrence while minimizing the rate of both Type I (false positive) and Type II (false negative) errors. We identified that (1) there were statistically significant differences between peak storm and triggering intensities, (2) the objectively defined threshold model presents a better balance between predictive success, false alarms and failed alarms than previous subjectively defined thresholds, (3) thresholds based on measurements of rainfall intensity over shorter duration (≤60 min) are better predictors of post-fire debris-flow initiation than longer duration thresholds, and (4) the objectively defined thresholds were exceeded prior to the recorded time of debris flow at frequencies similar to or better than subjective thresholds. Our findings highlight the need to better constrain the timing and processes of initiation of landslides and debris flows for future threshold studies. In addition, the methods used to define rainfall thresholds in this study represent a computationally simple means of deriving critical values for other studies of nonlinear phenomena characterized by thresholds.

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Notes

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    Any use of trade, firm or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.

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Acknowledgements

This research was made possible with funding from the U.S. Geological Survey Landslide Hazards Program and Multi-Hazards Demonstration Project. The authors are grateful for field assistance from Joseph Gartner (USGS), Maiana Hanshaw (USGS), and Robert Leeper (USGS), rainfall data provided by Pete Wohlgemuth (U.S. Forest Service), and data processing by Matthew Hansen (University of Colorado–Denver). Jonathan Godt, Rex Baum, and two anonymous reviewers have provided comments and suggested revisions which have greatly improved this paper.

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Correspondence to Dennis M. Staley.

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Staley, D.M., Kean, J.W., Cannon, S.H. et al. Objective definition of rainfall intensity–duration thresholds for the initiation of post-fire debris flows in southern California. Landslides 10, 547–562 (2013). https://doi.org/10.1007/s10346-012-0341-9

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Keywords

  • Debris flow
  • Wildfire
  • Rainfall
  • Thresholds
  • Warning system