This paper describes the development and validation of a spatio-temporal model for human-caused wildfire occurrence prediction at a regional scale. The study area is the 8028-km2 region of Madrid, located in central Spain, where more than 90% of wildfires are caused by humans. We construct a logistic generalised additive model to estimate daily fire ignition risk at a 1-km2 grid spatial resolution. Spatially referenced socioeconomic and weather variables appear as covariates in the model. Spatial and temporal effects are also included. The variables in the model were selected using an iterative approach, which we describe. We use the model to predict the expected number of fires in our study area during the 2002–05 period, by aggregating the estimated probabilities over space–time scales of interest. The estimated partial effects of the presence of railways, roads, and wildland–urban interface in forest areas were highly significant, as were the observed daily maximum temperature and precipitation.

Wildfire is an important system process of the earth that occurs across a wide range of spatial and temporal scales. A variety of methods have been used to predict wildfire phenomena during the past century to better our understanding of fire processes and to inform fire and land management decision-making. Statistical methods have an important role in wildfire prediction due to the inherent stochastic nature of fire phenomena at all scales.Predictive models have exploited several sources of data describing fire phenomena. Experimental data are scarce; observational data are dominated by statistics compiled by government fire management agencies, primarily for administrative purposes and increasingly from remote sensing observations. Fires are rare events at many scales. The data describing fire phenomena can be zero-heavy and nonstationary over both space and time. Users of fire modeling methodologies are mainly fire management agencies often working under great time constraints, thus, complex models have to be efficiently estimated.We focus on providing an understanding of some of the information needed for fire management decision-making and of the challenges involved in predicting fire occurrence, growth and frequency at regional, national and global scales.

We developed three models of daily human- and lightning-caused fire occurrence to support fire management preparedness and detection planning in the province of British Columbia, Canada, using a lasso-logistic framework. Novel aspects of our work involve (1) using an ensemble of models that were created using 500 datasets balanced (through response-selective sampling) to have equal numbers of fire and non-fire observations; (2) the use of a new ranking algorithm to address the difficulty in interpreting variable importance in models with a large number of covariates. We also introduce the use of cause-specific average spatial daily fire occurrence, termed baseline risk, as a covariate for missing or poorly estimated factors that influence human and lightning fire occurrence. All three models have strong predictive ability, with areas under the Receiver Operator Characteristic curve exceeding 0.9.

Fire danger systems have evolved from qualitative indices, to process-driven deterministic models of fire behavior and growth, to data-driven stochastic models of fire occurrence and simulation systems. However, there has often been little overlap or connectivity in these frameworks, and validation has not been common in deterministic models. Yet, marked increases in annual fire costs, losses, and fatality costs over the past decade draw attention to the need for better understanding of fire risk to support fire management decision making through the use of science-backed, data-driven tools. Contemporary risk modeling systems provide a useful integrative framework. This article discusses a variety of important contributions for modeling fire risk components over recent decades, certain key fire characteristics that have been overlooked, and areas of recent research that may enhance risk models.

For applications of stochastic fluid models, such as those related to wildfire spread and containment, one wants a fast method to compute time dependent probabilities. Erlangization is an approximation method that replaces various distributions at a time t by the corresponding ones at a random time with Erlang distribution having mean t. Here, we develop an efficient version of that algorithm for various first passage time distributions of a fluid flow, exploiting recent results on fluid flows, probabilistic underpinnings, and some special structures. Some connections with a familiar Laplace transform inversion algorithm due to Jagerman are also noted up front.

This paper presents an analysis of ignition and burn risk due to wildfire in a region of Ontario, Canada using a methodology which is applicable to the entire boreal forest region. A generalized additive model was employed to obtain ignition risk probabilities and a burn probability map using only historic ignition and fire area data. Constructing fire shapes according to an accurate physical model for fire spread, using a fuel map and realistic weather scenarios is possible with the Prometheus fire growth simulation model. Thus, we applied the Burn-P3 implementation of Prometheus to construct a more accurate burn probability map. The fuel map for the study region was verified and corrected. Burn-P3 simulations were run under the settings (related to weather) recommended in the software documentation and were found to be fairly robust to errors in the fuel map, but simulated fire sizes were substantially larger than those observed in the historic record. By adjusting the input parameters to reflect suppression effects, we obtained a model which gives more appropriate fire sizes. The resulting burn probability map suggests that risk of fire in the study area is much lower than what is predicted by Burn-P3 under its recommended settings.

The potential impact of climate change on forest fire risk is of significant concern. Postulated climate change effects on wildfires include increasing annual trends in ignitions and a lengthening of the fire season. We propose to use logistic generalized additive mixed models to investigate these characteristics. We present the modelling framework and outline a set of candidate models that are nested in terms of their fixed effects components. Model selection via likelihood ratio testing is discussed and connected to an entropy-based scoring rule for Bernoulli responses. We illustrate its application using data for lightning-caused forest fire ignitions over a period of 42 years in a 9 884 943 hectare region of boreal forest of northwestern Ontario, Canada. Seasonal and annual changes in ignition risk are observed and discussed, but we identify significant outstanding confounding factors that need to be addressed before one can assess the extent to which those changes can or cannot be attributed to climate change.

Results from studies of climate model scenarios suggest that forest fire ignitions will increase in Canada in the future because of climate change. Yet, there have been few studies that monitor long‐term trends in Canadian historical fire records. Although there are seasonal trends to historically reported fires within a fire season, there are also periods of zero‐heavy behaviour as well as periods during which more fires are reported than usual. We develop a flexible mixture‐modelling framework that permits the joint assessment of temporal trends in these dominant characteristics in terms of fire risk, defined as the daily probability that one or more fires are reported. The statistical power of such trend tests are also evaluated. We identify statistically significant increases in lightning‐caused fire risk between 1963 and 2009 in the boreal forest regions of the Rainy River and Lake of the Woods ecoregions in Northwestern Ontario, Canada. These observed changes in lightning‐caused fire risk were found to be associated with temperature and fire danger rating index anomalies. If such trends continue into the future, the duration of elevated periods of lightning‐caused forest fire risk is forecasted to increase by over 50% by the middle of this century. Copyright © 2014 John Wiley & Sons, Ltd.