Stochastic modelling of wind and its implication for wildfire spread predictions

Wildfire events have received much attention recently due to their serious socioeconomic impacts in countries like Australia, Canada, the United States and Greece.To tackle wildfire c rises, authorities and decision makers rely on a capability to obtain accurate and informative predictions of wildfire spread to support real time decision making, often with life or death consequences.However, the uncertainty inherent in wildfire model inputs, such as wind speed and direction, makes accurate prediction of wildfire s pread a c hallenging t ask.T o a ccommodate t he i nherent u ncertainties o f t he wildfire environment, wildfire m odellers a re i ncreasingly d rawing u pon p robabilistic o r e nsemble-based approaches to modelling fire s pread.For instance, Cruz [2010] used a Gaussian probability distribution function (PDF), with ensemble members sampled using a Monte Carlo approach, to simulate the variation of wind speed over a range of 27-78 km h -1 .In such simulations, spread prediction relies on different probable scenarios rather than a single set of input values.For example, the FireDST framework [French et al., 2014] samples input weather conditions from a uniform distribution, then visualizes the simulator output using burn probability maps, which provide useful information on the likelihood of different parts of the landscape being impacted by fire over a specific period of time [Pinto et al., 2016].Although ensemble-based approaches can potentially capture the uncertainty in the process of fire modelling, all of the approaches currently in use rely on deterministic simulators to derive burn probability maps.Deterministic simulators provide a single output from a given set of input conditions, and so do not faithfully represent the inherent stochasticity of real fire p ropagation.In this study, we consider an alternate modelling approach that better acknowledges the intrinsic uncertainties associated with wildfire spread.Wind speed and direction are critical inputs for bushfire simulation as a significant portion of the uncertainty in the wildfire modelling is caused by spatial and temporal variations in the wind.To capture this uncertainty, one can treat wind speed and direction as stochastic variables; this permits more faithful incorporation of the stochasticity of input variables into the simulation process, and provides a way of obtaining burn probability maps that better reflect the inherent uncertainties of wildfire prediction.A variety of stochastic processes can be used to model wind speed and direction.While it is still not known which process is the best to use in the context of wildfire simulation, we focused on two that have previously appeared in the wind and fire m odelling l iterature.T he Wiener p rocess h as u sed b y Z azali e t a l.[ 2017] to model fire s pread, w hile t he F irst-Order G auss-Markov p rocess ( also c alled t he O rnstein-Uhlenbeck (OU) process) has received a lot of attention in wind forecasting and for many other environmental factors [Edwards and Hurst, 2001].In this study, the Wiener and First-Order Gauss-Markov (FOGM) process models are employed to model wind speed and wind direction.The process noise δ of each process is calibrated using a series of data collected from eleven Davis Vantage Pro2 automatic weather stations that were set up at an experimental field site [Quill, 2017].The wind vector is then simulated by the two stochastic processes using the estimated values of the process noise for each of the two processes.In the final step, we evaluated the models by calculating the root mean square error (RMSE) and the standard deviation of the error (SDE), and compare the distributions of simulated data by stochastic models and the observed data.Finally, the stochastic wind models were incorporated within the SPARK fire simulation framework [Hilton et al., 2015], to produce representations of fire s pread b ased o n s tochastic w ind fi elds wi th th e calibrated process noise levels.The outcomes of the stochastic fire spread simulations provided a different interpretation of fire spread compared to simulations based on deterministic ensembles.

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