Visualization tools for assessing the Markov property: sojourn times in the forest Fire Weather Index in Ontario

摘要

In Canada, the Fire Weather Index (FWI) provides forest fire managers with an overall measure of fire danger. Specifically, the FWI is a numerical rating of the potential intensity of a forest fire based on its potential spread rate and the amount of vegetation available for combustion. In our analyses, we consider daily FWI time series, recorded over 42 fire seasons from a sample of fire-weather stations in Ontario, Canada. Graphical exploratory analyses of the data, including stalagmite plots (a new interactive, three-dimensional visualization tool), show that the FWI switches between epochs of nil and non-nil behaviour. This paper develops a framework for assessing sojourn times in these two phases. At some sites, the FWI process appears to begin each year as an approximate Markov process before gradually losing its Markovian character. However, a time-homogeneous discrete time Markov chain model is insufficient overall, because those sojourn times are not found to be geometrically distributed. Instead, the duration of epochs in each of these phases can be more accurately modelled using beta-geometric random variables which incorporate seasonality of phase-specific run length behaviour using local likelihood methods. Copyright (c) 2013 John Wiley & Sons, Ltd.