Rothermel's Model Research Articles

Towards predictive data-driven simulations of wildfire spread – Part I: Reduced-cost Ensemble Kalman Filter based on a Polynomial Chaos surrogate model for parameter estimation

Abstract. This paper is the first part in a series of two articles and presents a data-driven wildfire simulator for forecasting wildfire spread scenarios, at a reduced computational cost that is consistent with operational systems. The prototype simulator features the following components: an Eulerian front propagation solver FIREFLY that adopts a regional-scale modeling viewpoint, treats wildfires as surface propagating fronts, and uses a description of the local rate of fire spread (ROS) as a function of environmental conditions based on Rothermel's model; a series of airborne-like observations of the fire front positions; and a data assimilation (DA) algorithm based on an ensemble Kalman filter (EnKF) for parameter estimation. This stochastic algorithm partly accounts for the nonlinearities between the input parameters of the semi-empirical ROS model and the fire front position, and is sequentially applied to provide a spatially uniform correction to wind and biomass fuel parameters as observations become available. A wildfire spread simulator combined with an ensemble-based DA algorithm is therefore a promising approach to reduce uncertainties in the forecast position of the fire front and to introduce a paradigm-shift in the wildfire emergency response. In order to reduce the computational cost of the EnKF algorithm, a surrogate model based on a polynomial chaos (PC) expansion is used in place of the forward model FIREFLY in the resulting hybrid PC-EnKF algorithm. The performance of EnKF and PC-EnKF is assessed on synthetically generated simple configurations of fire spread to provide valuable information and insight on the benefits of the PC-EnKF approach, as well as on a controlled grassland fire experiment. The results indicate that the proposed PC-EnKF algorithm features similar performance to the standard EnKF algorithm, but at a much reduced computational cost. In particular, the re-analysis and forecast skills of DA strongly relate to the spatial and temporal variability of the errors in the ROS model parameters.

Analysis of Forest Fire Spread Trend Surrounding Transmission Line Based on Rothermel Model and Huygens Principle

With the expansion of the power grid, transmission lines across forests are increasing. Once forest fire occurs, it could threaten the transmission lines around or even cause them trip out. Therefore, studying the spread of forest fire is important. This paper presents a method based on Rothermel model and Huygens principle to analyze forest fire spread trend surrounding transmission line. Firstly, the principle of forest fire spread and the influence factors of the forest fire spread around transmission lines are analyzed. Then, based on Rothermel model and Huygens principle, the forest fires spread trends under three different conditions are simulated. By taking a transmission line of power grid in Shanxi Province as an example, the simulation is implemented and works out the average velocity and the consumed time during the forest fire spread from fire point to the transmission line under three different conditions. The result shows that the method is reasonable and valid.

An Implementation of the Rothermel Fire Spread Model in the R Programming Language

This note describes an implementation of the Rothermel fire spread model in the R programming language. The main function, ros(), computes the forward rate of spread at the head of a surface fire according to Rothermel fire behavior model. Additional functions are described to illustrate the potential use and expansions of the package. The function rosunc() carries out uncertainty analysis of fire behavior, that has the ability of generating information-rich, probabilistic predictions, and can be coupled to spatially-explicit fire growth models using an ensemble forecasting technique. The function bestFM() estimates the fit of Standard Fuel Models to observed fire rate of spread, based on absolute bias and root mean square error. Advantages of the R implementation of Rothermel model include: open-source coding, cross-platform availability, high computational efficiency, and linking to other R packages to perform complex analyses on Rothermel fire predictions.

Examination of the wind speed limit function in the Rothermel surface fire spread model

The Rothermel surface fire spread model includes a wind speed limit, above which predicted rate of spread is constant. Complete derivation of the wind limit as a function of reaction intensity is given, along with an alternate result based on a changed assumption. Evidence indicates that both the original and the revised wind limits are too restrictive. Wind limit is based in part on data collected on the 7 February 1967 Tasmanian grassland fires. A reanalysis of the data indicates that these fires might not have been spreading in fully cured continuous grasslands, as assumed. In addition, more recent grassfire data do not support the wind speed limit. The authors recommend that, in place of the current wind limit, rate of spread be limited to effective midflame wind speed. The Rothermel model is the foundation of many wildland fire modelling systems. Imposition of the wind limit can significantly affect results and potentially influence fire and fuel management decisions.

On large scale forest fires propagation models

The question of the modeling of forest fires at large scales is addressed. Empirical models are compared and it is shown that Rothermel's model describing the rate of spread of a straight front is included in the envelope model which in turn is included in a Hamilton–Jacobi equation description. This result shows that the preceding models could be included in reaction diffusion systems. Then an anisotropic propagation model with a nonlocal radiative term, obtained by asymptotic expansion of a combustion modeling, is proposed. This modeling takes into account the effects of wind and slope and it is shown that this type of modeling is the simplest generalization of the empirical ones.

Uncertainty propagation in wildland fire behaviour modelling

Rothermel's model is the most widely used fire behaviour model in wildland fire research and management. It is a complex model that considers 17 input variables describing fuel type, fuel moisture, terrain and wind. Uncertainties in the input variables can have a substantial impact on the resulting errors and have to be considered, especially when the results are used in spatial decision making. In this paper it is shown that the analysis of uncertainty propagation can be carried out with the Taylor series method. This method is computationally cheaper than Monte Carlo and offers easy-to-use, preliminary sensitivity estimations.

A Qualitative Comparison of Fire Spread Models Incorporating Wind and Slope Effects

Abstract Wind velocity and slope are two critical variables that affect wildland fire rate of spread. The effects of these variables on rate of spread are often combined in rate-of-spread models using vector addition. The various methods used to combine wind and slope effects have seldom been validated or compared due to differences in the models or to lack of data. In this study, rate-of-spread predictions from the Canadian Fire Behavior Prediction (FBP) system, McArthur's Mark V forest fire danger meter, the Rothermel empirical model, and the Pagni and Peterson physical model were compared with spread rates observed in a designed laboratory experiment in which wind velocity and slope were varied. Methods of combining wind and slope developed by Albini, McAlpine, and Rothermel were applied to two forms of Rothermel's model. Rothermel's model (original and modified) coupled with Albini's method and Pagni's model predictions closely reproduced the observed shape of the rate-of-spread response to wind and slope. Rothermel's method and McAlpine's method worked well in all cases except in upslope spread with opposed flow. However, Rothermel's model failed to predict a nonzero rate of spread in fuel beds with moisture contents of 35%. Possible causes of overprediction by McArthur's model and the FBP model included: (1) application of equations derived from full-scale fires to laboratory-scale fires, (2) improper selection of fuel type to represent artificial fuel beds, and (3) inaccurate estimation of wind velocity 10 m above the vegetation surface using a logarithmic profile. For. Sci. 43(2):170-180.

Fire Behavior Experiments in Mixed Fuel Complexes

A series of laboratory fire experiments were conducted in fuel beds consisting of either excelsior (wood wool), or 6.35 mm sticks, or a mixture of these. Tests were done both with and without wind. Various characteristics of the fire, including rate of spread and fireline intensity, were compared with predictions from the Rothermel model. The behavior of the mixed fuel fires, compared to that of the fires in the constituent fuels, did not agree well with the predictions of the model. We conclude that, in order to model the behavior of fire in mixed fuels, the Rothermel model needs modification.

Bushfire rate‐of‐spread forecasting: Deterministic and statistical approaches to fire modelling

AbstractThe three basic modelling approaches used to explain forest fire behaviour are theoretically, laboratory or empirically based. Results of all three approaches are reviewed, but it is noted that only the laboratory‐ and empirically based models have led to forecasting techniques that are in widespread use. These are the Rothermel model and the McArthur meters, respectively. Field tests designed to test the performance of these operational models were carried out in tropical grasslands. A preliminary analysis indicated that the Rothermel model overpredicted spread rates while the McArthur model underpredicted. To improve the forecast of bushfire rate of spread available to operational firefighting crews it is suggested that a time‐variable parameter (TYP) recursive least squares algorithm can be used to assign weights to the respective models, with the weights recursively updated as information on fire‐front location becomes available. Results of this methodology when applied to US Grasslands fire experiment data indicate that the quality of the input combined with a priori knowledge of the performance of the candidate models plays an important role in the performance of the TVP algorithm. With high‐quality input data, the Rothermel model on its own outperformed the TVP algorithm, but with slightly inferior data both approaches were comparable. Though the use of all available data in a multiple linear regression produces a lower sum of squared errors than the recursive, time‐variable weighting approach, or that of any single model, the uncertainties of data input and consequent changes in weighting coefficients during operational conditions suggest the use of the TVP algorithm approach.

Modelling Moisture Damping for Fire Spread in a Mixture of Live and Dead Fuels

A model, based on those of Rothermel(1972) and Wilson (1990), is developed for the effect of fuel moisture on fire spread rate in a fuel complex consisting of a mixture of live and dead fine fuel particles. Physical arguments lead to a modification of the heat sink term of Rothermel's model. A form of moisture damping is proposed which generalises that of Wilson. It uses one extra parameter, which needs to be estimated from experimental burns in a mixture of live and dead fuels. The model is fitted to a series of experimental shrubland fires. The model fits this data better than does Rothermel's original model, but is not yet recommended for use by practitioners.

Fire History and Potential Fire Behavior in a Rocky Mountain Foothill Landscape

A landscape approach was used to study fire history and fire behavior in the Douglas-fir forests and foothill vegetation of the Bighorn Canyon National Recreation Area in southcentral Montana. The 3,976 ha study area was divided into 4-ha grid cells, and traditional fire scar analysis and fuel sampling methods were used for data collection in each cell. There have been 15 surface fires during the last 109 years and 10 canopy fires during the last 360 years. The mean fire interval in the forests as a whole, was 7 years for surface fires and 31 years for canopy fires. Using the Weibull function, the recurrent time for fire in a specific grid cell was 212 and 226 years for surface and canopy fires, respectively. The distribution of the probability density function showed that there was a peak of high canopy fire frequency between 150-250 years of stand age. There was no obvious peak period for surface fires in humid ravines, which suggests that surface fires there are not associated with aging. Employing Rothermel's model, a fire behavior model (FIREMDL) was developed and linked it to a geographic information system (GRASS) to simulate flammability of each grid cell under different conditions of fuel moisture and wind velocity. The results suggest that flammability is highly variable because of differences in vegetation and topographic position.

The Effects of Alien Shrub Invasions on Vegetation Structure and Fire Behaviour in South African Fynbos Shrublands: A Simulation Study

(1) South African fynbos vegetation is fire-prone and susceptible to invasion by alien shrubs. Alien shrubs change the nature of the fuel bed and thus affect fire behaviour. (2) Changes in biomass, size and distribution of plant parts as fuel and plant moisture and energy contents were determined at two sites invaded by the important alien shrubs Hakea sericea Schrad. and Acacia saligna (Labill.) Wendl. (3) The data were used to define fuel models and to simulate fire behaviour using Rothermel's fire model. This simulation was used to test the hypothesis that invasion increases fire hazard through increasing fuel loads. (4) Invasion by H. sericea resulted in a 60% increase in fuel load and lowered the moisture content of live foliage from 155 to 110%. Simulated rates of fire spread and intensity were nonetheless lower than in fynbos due to a densely-packed fuel bed. (5) Invasion by A. saligna resulted in a 50% increase in fuel load. The high moisture content of foliage of this shrub (about 270%) effectively reduces the fuel load and fuel bed depth, resulting in low rates of fire spread and intensity in the simulation. (6) Shortcomings in Rothermel's model prevented the accurate simulation of high intensity fires which have occurred in invaded areas under extreme weather conditions. Such fires vigorously consume the increased biomass of shrub crowns, are difficult to content of foliage of this shrub (about 270%) effectively reduces the fuel load and fuel bed Under such conditions, the fire hazard will be increased by invasion.

Fire Behaviour in South African Fynbos (Macchia) Vegetation and Predictions from Rothermel's Fire Model

(1) South African fynbos (sclerophyllous shrubland) vegetation is fire-prone, and fire is important in fynbos management. No data on fire behaviour in fynbos are presently available. (2) The behaviour of fourteen experimental fires in fynbos tall open shrublands is described. Rates of spread ranged from 0.04 to 0.89 m s-1, flame lengths from 2 8 to 7.0 m and fire intensities from 515 to 20 709 kW m-1. (3) The fire behaviour is compared to predictions from Rothermel's fire spread model, which uses fuel characteristics and environmental conditions to predict fire spread and intensity. Predictions of rate of spread and flame length were good but fire intensity was underestimated where biomass and fire hazard were high. (4) The results are compared to fire behaviour in other shrubland ecosystems. Rates of fire spread and fire intensity are greater in fynbos than in Scottish heathland, and are equivalent to those reported for Californian chaparral. (5) The inclusion of fire danger indices and predictions based on Rothermel's model in fynbos fire records will enhance their value. The model can also be useful in fire research, particularly in homogenous vegetation, and represents an improvement on techniques such as the measurement of fire temperature.

Fuel characteristics of arctic plant species and simulated plant community flammability by Rothermel's model

The relative fuel-potentials of 12 northern tundra and forest–tundra ground species of the Mackenzie delta area were evaluated from measured fuel characteristics by simulating a test fire with the Rothermel (1972) fire behavior model. The relative importance of the fuel parameters were in decreasing order: moisture content, biomass, fineness (surface/volume ratio), packing ratio, silica-free ash content, and caloric content. The fuel-potential ratings of the vascular species and of the communities were differentiated primarily by their leaf characteristics. Dead leaves of Calamagrostis canadensis and Eriophorum vaginatum constituted the most flammable fuels measured. Evergreen Ledum palustre and Empetrum nigrum were clearly differentiated from the live vascular species by higher flammability ratings. Of the cryptogam fuels, Cladonia-type lichens were rated intermediate between the above evergreen ericoids and the deciduous woody species (Betula glandulosa, Vaccinium uliginosum, Salix glauca), while Sphagnum sp. was rated comparable to the latter groups. Epilobium angustifolium received the lowest ratings of all species.Subject to the limitations with respect to ether-extractive contents, the relative fuel potential of tundra and forest–tundra plant communities can be rated on measured fuel characteristics, community composition, and the criteria of the Rothermel model. Possible applications of this study were raised, particularly the use of relatively nonflammable plants in land management.