Explaining Return Times for Wildfires

Abstract

Our interest is in analyzing fire regimes in the Mediterranean ecosystem in the Cape Floristic Region of South Africa (CFR). With this objective, we consider an extensive database of observed fires with high-resolution meteorological data during the period 1980–2000 to build a novel survival model. The model is constructed as a time-to-event specification incorporating space- and time-varying covariates along with spatial random effects. With data at grid cell level, conditionally autoregressive (CAR) modeling is used for the spatial random effects. However, areal sampling is very irregular, yielding disjoint sets of areal units. Hence, disappointingly, the spatial model does not improve upon the nonspatial version. Results regarding the covariates reveal an important influence of seasonally anomalous weather on fire probability, with increased probability of fire in seasons that are warmer and drier than average. In addition to these local-scale influences, the Antarctic Ocean Oscillation (AAO) is identified as a potentially important large-scale influence on precipitation and moisture transport. Fire probability increases in seasons during positive AAO phases, when the subtropical jet moves northward and low-level moisture transport decreases. We conclude that fire occurrence in the CFR is strongly affected by climatic variability at both local and global scales. Thus, there is the suggestion that fire risk is likely to respond sensitively to future climate change. Comparison of the modeled fire risk/probability across four 12-year periods (1951–1963, 1963–1975, 1975–1987, 1987–1999) provides some supporting evidence. If, as currently forecast, climate change in the region continues to produce higher temperatures, more frequent heat waves, and/or lower rainfall, our model thus indicates that fire frequency is likely to increase substantially. This article extends earlier work by Wilson et al. (2010).

AMS Subject Classification:

• 62F15

Keywords:

• CAR model
• Hierarchical model
• Markov-chain Monte Carlo
• Probit link
• Time-to-event model

Notes

1. 1. The choice of 25% was an ecological one and can be viewed as illustrative. Other thresholds could be investigated so that sensitivity could be assessed.

2. 2. We have not considered time-indexed spatial effects since, with 192 time intervals, this would introduce 192 CAR models, much more than the data can support.

3. 3. We assume that at every site there will eventually be a fire or a fire after an observed fire. The notion of a “cure rate” (Berkson and Gage 1952; Maller and Zhou 1996) does not seem sensible for fire occurrence.