Statistical modeling of rare stochastic disturbance events at continental and global scales: post-fire debris flows and wildland fires

Chapter 1: Frequency-magnitude distribution of debris flows compiled from global data, and comparison with post-fire debris flows in the western U.S. Forecasting debris flow hazard is challenging due to the episodic occurrence of debris flows in response to stochastic precipitation and, in some areas, wildfires. In order to facilitate hazard assessment, we have gathered available records of debris flow volumes into the first comprehensive global catalog of debris flows (n = 988). We also present results of field collection of recent debris flows (n = 77) in the northern Rocky Mountains, where debris flow frequency increases following wildfire. As a first step in parameterizing hazard models, we use frequency-magnitude distributions and empirical cumulative distribution functions (ECDFs) to compare volumes of post-fire debris flows to non-fire-related debris flows. The ECDF of postfire debris flow volumes is significantly different (at 95% confidence) from that of non-fire-related debris flows, suggesting that the post-fire distribution is composed of a higher proportion of small events than that of non-fire-related debris flows. The slope of the frequency-magnitude distribution of post-fire debris flows is steeper than that of non-fire-related debris flows, corroborating evidence that small post-fire debris flows occur with higher relative frequency than non-fire-related debris flows. Taken together, the statistical analyses suggest that post-fire debris flows come from a different population than non-fire-related debris flows, and their hazard must be modeled separately. We propose two possible non-exclusive explanations for the fact that the post-fire environment produces a higher proportion of small debris flows: 1) following fires, smaller storms or effective drainage areas can trigger debris flows due to increased runoff and/or decreases in root strength, resulting in smaller volumes and increased probability of failure, 2) fire increases the probability and frequency of debris flows, causing their distribution to shift toward smaller events due to limitations in sediment supply. Chapter 2: The relationship of large fire occurrence with drought and fire danger indices in the western US: the role of temporal scale The relationship between large fire occurrence and drought has important implications for fire hazard prediction under current and future climate conditions. The primary objective of this study was to evaluate correlations between drought and fire-danger-rating indices representing short- and long-term drought, to determine which had the strongest relationships with large fire occurrence at the scale of the western United States during the years 1984-2008. We combined 4-8 km gridded drought and fire-danger-rating indices with information on fires greater than 1000 acres from the Monitoring Trends in Burn Severity project. Drought and fire danger indices analyzed were: monthly precipitation (PPT), Energy Release Component for fuel model G (ERC(G)), Palmer Drought Severity Index (PDSI), 3-month Standardized Precipitation Index (SPI3), SPI6 , SPI9, SPI12, and SPI24. To account for differences in indices across climate and vegetation assemblages, indices were converted to percentile conditions for each pixel, to indicate the relative anomaly in conditions during large fires. Across the western US, correlations between area burned and short-term indices ERC(G) and PPT percentile were strong (R2 = 0.92 and 0.89 respectively), as were correlations between number of fires and these indices (R2=0.94 and 0.93 respectively). As the period of time tabulated by the index lengthened, correlations between fire occurrence and indices weakened: PDSI and 24-month SPI percentile showed weak or negligible correlations with area burned (R2 = 0.25 and -0.01 respectively) and number of large fires (R2 = 0.3 and 0.01 respectively). This result suggests the utility of shorter-t