Prediction of spatially explicit rainfall intensity–duration thresholds for post-fire debris-flow generation in the western United States
Introduction
Over the past several decades, the frequency of large wildfires, length of fire season, and duration of individual wildfires have steadily increased in the western United States as a result of a combination of human activities, evolving land-use patterns, weather, and climate (Westerling et al., 2006). An increase in the susceptibility to debris flow is a secondary effect of wildfire in recently burned steeplands, a hazard which may persist for several years following fire containment (Cannon and DeGraff, 2009, Cannon et al., 2010, DeGraff et al., 2015). Risk associated with debris-flow hazards increases as populations expand into foothill and mountainous areas susceptible to wildfire. In addition, a greater incidence of fire activity in mountainous areas with relatively infrequent fire recurrence may increase the potential of debris flows in environments or communities where debris-flow hazard has been historically absent (Cannon and DeGraff, 2009). The geographic expansion of areas exposed to post-fire debris-flow hazard has motivated efforts to reduce exposure of people, infrastructure, and important natural, cultural, and economic resources to these hazards. Hazard assessment provides the first step in reducing public exposure to these events, as this process identifies areas vulnerable to post-fire debris-flow generation, and provides estimates of the magnitude of an event, should one occur (Cannon et al., 2008, Cannon et al., 2010, Cannon et al., 2011, Staley et al., 2013a, Staley et al., 2013b, Staley et al., 2013c).
In the western United States, the most common methods for post-fire debris-flow hazard assessment are based upon statistical models that predict the likelihood and magnitude of debris flow for a specific location using historical data (Gartner et al., 2008, Gartner et al., 2014, Cannon et al., 2010). These hazard assessments (e.g. Cannon et al., 2009, Parise and Cannon, 2012, USGS, 2016) are useful for identifying and prioritizing areas of potential debris-flow hazard for planning purposes, but are not intended for direct predictive use in early warning systems (Cannon et al., 2010). Instead, post-fire debris-flow early warning in the western United States relies upon regionally specific rainfall intensity–duration thresholds (Cannon et al., 2008, Cannon et al., 2011, Staley et al., 2013b, Staley et al., 2015). Regional thresholds are determined from historical data that characterize the rainfall intensities that produced, or did not produce, debris flows for specific locations. The empirical approach for establishing regional rainfall intensity–duration thresholds requires an extensive library of rainfall and basin response information from which the thresholds can be calculated by either subjective (e.g. Cannon et al., 2008, Cannon et al., 2011) or objective methods (Staley et al., 2013b, Staley et al., 2015).
Empirically derived rainfall intensity–duration thresholds for the generation of runoff-induced post-fire debris-flows in southern California (Cannon et al., 2008, Cannon et al., 2011, Staley et al., 2013b) compose a major component of the U.S. Geological Survey (USGS) and the National Oceanic and Atmospheric Administration (NOAA) post-fire debris-flow early warning system, currently operating in the National Weather Service (NWS) Los Angeles–Oxnard and San Diego weather forecasting offices (NOAA, 2005). Intensive research and monitoring over a span of > 10 years was needed to define regional thresholds sufficiently robust for inclusion in a warning system. This system involved the comparison of forecasted and real-time estimates of rainfall intensity to preexisting intensity–duration thresholds. How closely the forecasted or observed rainfall rates compare to the threshold values are a major factor in the decision-making process for issuing debris-flow outlooks, watches, and warnings (USGS, 2005). The success of the early warning system in southern California has resulted in significant interest in the expansion of the program to other fire-prone regions of the United States; however, expansion using the current framework is hampered by time-consuming development of regional rainfall thresholds.
In an effort to expand operational capabilities to areas with no established regional intensity–duration thresholds, we develop and test a new framework that integrates statistical methods of characterizing debris-flow susceptibility with empirical methods for determining rainfall intensity–duration thresholds. Specifically, our new framework combines approaches for calculating the statistical likelihood of post-fire debris flows using logistic regression with objective techniques for defining rainfall intensity–duration thresholds. The combination provides a single method that can (1) predict the likelihood that a debris flow will occur at a given rainfall intensity, and (2) define accurate, spatially explicit rainfall thresholds, which correspond to the rainfall intensity that results in a 50% likelihood of debris flow.
Section snippets
Post-fire debris-flow hazard prediction
The prediction of runoff-induced post-fire debris-flow occurrence has traditionally relied upon statistical methods that calculate a likelihood of debris-flow generation in response to rainfall of a given intensity using logistic regression (Rupert et al., 2008, Cannon et al., 2010) and the identification of rainfall rates that correspond to increased probability of debris-flow occurrence during a rainstorm using empirical rainfall intensity-duration thresholds (Cannon et al., 2008, Cannon et
Conceptual model of post-fire debris-flow generation and likelihood
Previously, logistic regression models of post-fire debris-flow generation (e.g. Rupert et al., 2008, Cannon et al., 2010) relied upon a stepwise statistical approach for variable selection. Model success was measured solely upon statistical performance. While this approach provided an objective, non-biased method for variable selection and evaluation of model performance, the physical relevance of the variables and their effects on model predictions of likelihood were sometimes
Methodology
This study relied upon the established methods of logistic regression (Eqs. (1), (2)) and receiver operating characteristics (ROC) analysis (Swets, 1988, Fawcett, 2006) to develop a new method for the spatially explicit prediction of rainfall intensity-duration thresholds. Logistic regression models were based upon empirical data collected within the first two years of wildfire in recently burned areas in the western United States (Fig. 1 and Table 3). In total, the database used for this study
Results and discussion
Our selection criteria outlined above resulted in the identification of four potential logistic models (M1, M2, M3 and M4). Variables, intercept values, and coefficient values for each model are listed in Table 4. Statistical and ROC performance measures for the training and test datasets, and existing regional thresholds, are reported in Table 5.
In the following sections we discuss (1) the results of the model calibration and evaluation of sensitivity based on the training dataset, (2) the
Conclusions
By merging traditional approaches for debris-flow susceptibility mapping with rainfall threshold identification, this paper described a new fully predictive framework for assessing post-fire debris flow hazards using free, readily available geospatial data. Our approach can be used to predict rainfall intensity–duration thresholds for recently burned areas in the western United States where there are no preexisting historical data concerning rainfall rates responsible for post-fire debris-flow
Acknowledgments
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 the field assistance from Joseph Gartner, Kevin Schmidt, Anne-Marie Matherne, Maiana Hanshaw, Robert Leeper, and Octavanio Lucero, and for the rainfall data provided by Pete Wohlgemuth and Terri Hogue. We also would like to acknowledge Sue Cannon for her seminal work defining rainfall intensity–duration thresholds for
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