Forest Fire Spread Simulation and Fire Extinguishing Visualization Research

Abstract

There are three main types of forest fires: surface fires, tree crown fires, and underground fires. The frequency of surface fires and tree crown fires accounts for more than 90% of the overall frequency of forest fires. In order to construct an immersive three-dimensional visualization simulation of forest fires, various forest fire ignition methods, forest fire spread, and fire extinguishing simulation exercises are studied. This paper proposes a lightweight forest fire spread method based on cellular automata applied to the virtual 3D world. By building a plant model library using cells to express different plants, and by building a 3D geometric model of plants to truly capture the combustion process of a single plant, we can further simulate forest-scale fire propagation and analyze the factors that affect forest fire spread. In addition, based on the constructed immersive forest scene, this study explored various forms of fire extinguishing methods in the virtual environment, mainly liquid flame retardants such as water guns, helicopter-dropped flame retardants, or simulated rainfall. Therefore, the forest fire occurrence, spread, and fire extinguishing process can be visualized after the interactive simulation is designed and implemented. Finally, this study greatly enhanced the immersion and realism of the 3D forest fire scene by simulating the changes in plant materials during the spread of a forest fire.

1. Introduction

In recent years, forest fires have become prevalent natural disasters that countries, regions, and organizations around the world need to face [1]. Therefore, researchers have explored the principles of forest fire behavior to reduce the damage caused by forest fires to the national economy and the ecological environment, such as when Hädrich [2] fit the three-dimensional geometric modeling of plants to capture the burning of individual trees and the propagation between trees; that of Pais [3] models units based on fuel, weather, humidity, and terrain attributes, further facilitating the prediction of the growth of individual fires. Forest fire simulation and fire scene reproduction, prediction, and disaster assessment have become research hotspots in forestry virtual simulation. Due to the complexity, particularity, danger, and destructiveness of the forest environment and forest fire experiments, obtaining relevant fire scene data and fire-fighting decision-making drills through real ignition experiments is difficult. Therefore, this paper uses advanced visualization and virtual reality technology to build an immersive three-dimensional visualization simulation of forest fires, realize the research on various forest fire ignition methods and forest fire spread, and provide support for fire extinguishing simulation drills.

Forest fire spread has always been a complex and difficult process to model, but Hädrich [2], Pais [3], and Meng [1] et al still propose fire simulation models suitable for different conditions. Sullivan, A.L. [4,5,6] conducted extensive and in-depth discussions on the methods of these researchers, categorized the construction methods of the models reasonably, and further helped us understand the relevant concepts of forest fire models, which are mainly summarized into three categories: physical models, empirical models, and semi-empirical models.

The criteria for classification are whether the model is based on a statistical analysis of experimentally obtained data and whether it involves chemical or physical principles of combustion and fire diffusion processes. In addition to choosing a flame simulation model, researchers who want to visualize the forest fire spread process must also select a corresponding spread method. These methods can be divided into two categories, including grid-based simulation and vector-based simulation. Grid-based simulations are typified by cellular automata, which can expand fire boundaries based on direct contact or neighbor spread. The vector-based simulation is represented by the Huygens principle, which models the propagation of the fire front as a wave and describes the stretch of the fire boundary by its boundary moving forward in time and space. This paper is mainly based on the Chinese Wang Zhengfei model to calculate the speed of forest fire spread and uses cellular automata to express the spread of forest fire in 3D virtual scenes.

In the process of forest fire spread, fire intensity is the primary fire behavior characteristic that expresses the impact of forest fire on related resources. In contrast, flame spread rate and length are critical parameters for fire intensity. The fuel, topography, and weather mainly influence these parameters. The fuel’s moisture content significantly affects the ignition and fire spread characteristics during pyrolysis [7,8,9]. In contrast, the moisture content of the fuel depends mainly on long-term and short-term meteorological conditions [10]. In particular, air temperature, air humidity, and precipitation, among other weather factors, have a decisive impact on the water content of combustibles, and the strength and direction of the wind also affect the range and demand of forest fire spread [1,11,12]. Liu et al. [13] quantified the relative importance of combustibles, topography, and weather on fire spread at different spatial scales to determine fire size thresholds; in Carmen Awad et al. [4], moisture thresholds were explored; Rachael H. Nolan et al. [14] explored in detail the link between plant responses to drought and forest flammability, providing insights into forest fires and new predictive models of seasonal fuel dynamics; and MATTHEWS et al. [9] also answered the impact of climate change on fuel quantity, fuel humidity, and fire behavior, and further compared whether it had a significant effect on the weather and on fire behavior. In addition, terrain factors include slope, altitude, and aspect, but the impact of altitude on forest fire spread cannot be directly expressed on relatively flat terrain. Therefore, to consider the effect of terrain, this study takes slope as the primary terrain factor that directly affects the forest fire spread.

In simulation studies of forest fire occurrence, spread, and fire fighting in one-dimensional and two-dimensional scenes [15,16,17], the visualization process is relatively rough. It cannot provide a realistic and immersive experience. Therefore, in the 3D forest scene, it is of great value to realize the simulation of forest fire occurrence, spread, and fire extinguishing. For example, Huang et al. [18] successfully constructed a visualization of the forest under climate change in a 3D scene based on a data drive, which can help determine the relationship between forest fire frequency and climate change, and this provides the basis for providing an immersive experience for visualizing the spread of forest fires and the fire suppression process.

A forest fire spread model based on this construction can help design and implement fire fighting behaviors and visualize the fire fighting process through human participation and joint forestry equipment, fire retardants, and aviation assets [19]. This visualization, when applied in real-time to help plan fire strategies and training, not only supports the training of firefighters and managers and helps improve fire control and prevention, land management, and firefighter distribution-based training strategies, but it is also used as a decision aid to provide decision support [20,21]. Therefore, this paper explores the impact of flame retardants on flame spread by visualizing fire extinguishing behaviors, which mainly includes spraying flame retardants with water guns and helicopters and simulating rainfall.

In addition, based on the physical model and considering the feedback to the atmosphere in the process of forest fire spreading, it is possible to realize forest fire spreading with a strong sense of reality in the 3D scene, but it is necessary to design related equations between the forest fire and the atmosphere. Their solutions require high computing power [22,23]. Therefore, to realize the real-time visualization of forest fire occurrence, spread, and fire extinguishing processes in the three-dimensional virtual scene, the complexity and processing time of the algorithm must be reduced to design an algorithm to obtain the result of forest fire spread quickly. Therefore, this paper proposes a lightweight forest fire spread model applied to the 3D virtual world that minimizes the complex calculation process while pursuing the visualization results and ensuring the realism of forest fire behavior and the immersion of the virtual environment.

In summary, the contributions of this paper are as follows:

(1)

This paper proposes a forest fire spread model based on cellular automata. By considering the influence of combustibles, weather, and terrain, it successfully visualizes a forest fires’ occurrence, spread, and extinguishing behavior in a virtual 3D scene.

(2)

By constructing different combustible models and obtaining weather factors such as wind, humidity, and temperature, this paper controls forest fire behavior and realizes the mutual transition between surface and crown fire.

(3)

By simulating the temperature change during the combustion of combustibles, this paper further visualizes the fire extinguishing process of liquid flame retardants to explore the way they affect the spread of forest fires; these include water guns, helicopters dropping flame retardants, and simulated rainfall.

(4)

Based on the texture mixing technology, this paper simulates the change in vegetation material during the flame-burning process, enhancing the sense of reality and immersion in the virtual 3D environment.

The structure of this paper is as follows. Section 1 introduces the background and significance of the forest fire spread model. Section 2 reviews related research in the field of forest fire spread simulation. Section 3 summarizes the research contents and methods of this paper. Section 4 details the plant model library, the cellular automata modeling approach, and the principles of fire fighting behavior. Section 5 carries on the algorithm design and implementation. Section 6 describes the findings and discusses them. Finally, Section 7 describes the strengths and weaknesses of this study in light of the relevant results and provides an in-depth outlook on future work.

2. Related Research

Studies have shown that the spread of forest fires depends on static factors such as topography and vegetation type and is also a dynamically driven process influenced by weather factors [24]. The spread of forest fires is mainly related to weather, terrain, and combustible factors. Based on the above factors and the principle of cellular automata, this paper realizes the visualization of forest fire spread and fire extinguishing behavior in a 3D environment and further explores the principles of forest fire spreading and extinguishing. Still, large-scale forest and terrain modeling are not considered.

2.1. Weather, Terrain and Fuel Characteristics

After the researchers’ exploration, it can be determined that the behavior and intensity of forest fires depend on weather, terrain, and fuel characteristics. Weather factors strongly influence forest burning and fire behavior, especially wind, ambient temperature, and relative humidity [25]. Wind speed and wind direction control the speed and direction of fire spread, and high temperatures significantly impact surface vegetation; that is, they affect the dynamic changes in the moisture content of combustibles, and the lower the relative humidity, the lower the moisture content of combustibles. This further leads to the faster drying of combustibles. In addition, many studies on forest fire spread models have also shown that the behavior of forest fire spread also depends on the physical properties of combustibles, such as the water content and load of plants, etc. [26,27], and the influence of terrain on forest fire spread has never been ignored. Therefore, as three important factors affecting forest fires, researchers have discussed and studied the impact of weather, terrain, and fuel characteristics on forest fire behavior [25,26,27,28].

2.2. Fire Models

The forest fire spread model is essential to the forest fire spread simulation technology. After the researchers digitize the parameters affecting the fire, the forest fire spread model constructed can express the relationship between forest fire behavior and parameters and the quantitative relationship between them. Based on whether the model is based on a statistical analysis of experimentally obtained data and whether it involves chemical or physical principles of combustion and fire spread processes, existing fire spread models can be divided into three categories: physical models, empirical models, and semi-empirical models [1,4,5,6].

2.2.1. Empirical Models

The empirical model refers to the model equation mainly based on the statistical analysis of the data obtained by the experiment and is based on observation and experiment rather than theory. The model usually intuitively describes the key characteristics of fire behavior, such as the head flame’s forward spread rate and the flame’s height and angle. Based on the ignition experiment and combined with the actual fire observation data, the quantitative relationship between the fire behavior characteristics and each parameter has been derived and successfully constructed [23,24]. Many excellent forest fire spread models have been derived based on the Canadian forest fire spread model. For example, the Prometheus [29] model calculates the fire spread rate and other fire behavior characteristics by using the Canadian forest fire spread model, and it expands some types of combustibles. The Cell2Fire fire growth simulator developed by Pais et al. [3] is based on the spread rate predicted by the Canadian forest fire spread model to control the fire spread trend of each unit in the fire environment. The simulator not only has better prediction effect, but also has a simulation speed that is fast and highly scalable.

2.2.2. Physical Models

A model based on the chemical or physical principles of combustible combustion and fire diffusion process is called a physical model. This type of model is usually based on the law of physical conservation and uses heat radiation as the main heat transfer method to convert the prediction problem of flame spread speed to Calculation problems for heat conduction followed by the establishment of the differential equation for heat diffusion [5]. To build a more complete forest fire spread model, it is necessary to conduct in-depth research on the physical and chemical phenomena of the forest fire combustion process.

Therefore, researchers [12,30] have improved the accuracy of the model by integrating cellular automata with physical models, and while simplifying the modeling of complex combustibles, the fire boundary spread behavior is explored in detail. Pirk et al. [31] performed a detailed physical simulation of the important role of carbon insulation in forest fire combustion after studying the process of wood pyrolysis in forest fire combustion behavior. You et al. [32] optimized the model of Pirk et al. [31] based on the principle of finite state machine, enabling further research on the physical mechanism of the forest fire burning process. In addition, Hädrich et al. [2] realized the simulation of single wood burning in fire by coupling the forest fire combustion process with the solver in the heat transfer process of changing ambient temperature. So, this method can not only simulate forest fire propagation more realistically, but also realize the selection of different levels of detail for forest fire simulation.

2.2.3. Semi-Empirical Models

Semi-empirical models are usually based on existing empirical or physical models and describe the behavior of forest fire spread in the entire scene through mathematical simulation. Typical semi-empirical models include the Chinese Wang Zhengfei mode [21,24] and the American Rothermel model [33,34], etc. The Wang Zhengfei model was constructed through multiple ignition experiments combined with the physical principles of forest fire combustion. The Rothermel model was created based on observing the law of material conservation; it is designed according to the physical mechanism in the forest fire spreading process. It is established after statistical analysis of the experimental results in specific experiments.

Wang Zhengfei’s model is more suitable for China’s forest fire simulation and prediction. For example, Wang et al. [35] analyzed the model and used the nonlinear least squares method to re-fit the wind speed correction coefficient to obtain a result closer to the actual value. The improvement of the provincial forest fire spread model provides the basis. Zechuan Wu et al. [24] established a forest fire spread prediction model combining cellular automata and Wang Zhengfei’s model and compared it with the artificial neural network model to further provide more practical forest fire prediction and management in Heilongjiang Province. Fire propagation model. In addition, the method of Zhou et al. [36] based on the Wang Zhengfei model approximated the spread of forest fires, and compared with the traditional Rothermel model, a relatively real result of forest fire spread was obtained. Liu et al. [37] used the Wang Zhengfei model to obtain the initial spread speed of forest fires after constructing the real 3D terrain, which reflected the spread characteristics of forest fires well.

The Rothermel model has a high degree of abstraction and has a wide range of applications. The input of multidimensional parameters (combustibles, terrain, weather, etc.) will lead to uncertainty problems. Therefore, to solve such problems, researchers also made some explorations. For example, Kc et al. [38] conducted a comprehensive sensitivity analysis of the input parameters of the Rothermel model and further discussed and explained the impact of the sensitivity index value on the fire model; Jorge et al. [39] also considered the complexity of forest fire phenomena and some input parameter values. Uncertainty, a meta-heuristic algorithm, was used to calibrate the input parameters from the Rothermel model, thus helping to provide accurate fire spread predictions. Valero et al. [40,41] used multi-fidelity techniques to overcome uncertainties in wildfire behavior predictions and evaluated the applicability of multi-fidelity methods to quantify uncertainties in wildfire simulations. Finally, in Yuan et al. [42], a comprehensive parameter uncertainty analysis was performed for a representative model.

2.3. Space Fire Spread

Researchers who realize forest fire behavior simulation in two-dimensional or three-dimensional spaces based on visualization and virtual reality technology need to choose an appropriate forest fire spread method to express the spread of forest fire in an area after the forest fire spread model is successfully constructed. There are mainly two types of spatial representations, vector data and raster data, for simulating the spatial spread of forest fires. Vector models are usually based on Huygens’ principle, while grid models generally use cellular automata [1,6,30].

2.3.1. Huygens Principle

The Huygens principle, which can describe the evolution of the shape of the fire front based on vector data, was proposed to explain light waves as early as the seventeenth century. By considering the fire boundary as a closed curve connecting the points, each point of the fire boundary is regarded as a new fire source based on the given fire spread model and the condition of the new fire source location [6], and it performs turbulent fluid flow calculations to simultaneously determine the temperature field and the spread of the fire [15].

The FARSITE fire field growth simulator based on the fire behavior prediction system of the U.S. Forest Service is a vector-based Huygens-type model. The movement mechanism of the gradient wind flow is incorporated into the model [3]. Zhou et al. [43] proposed a new method to simultaneously estimate the fire perimeter and fuel adjustment factor of the FARSITE fire model, thereby achieving an accurate prediction of forest fire spread. Zhang et al. [44] simulated real wildfire behavior based on the FARSITE fire model and further discussed the application of UAVs in wild forest fire search and fire front monitoring tasks. Ge et al. [33] used ArcGIS’s powerful graphics processing capabilities and spatial analysis capabilities to simulate forest fire propagation by combining the Rothermel model with Huygens’ principle and graphically expressing the propagation process, thereby improving the usability and reliability of the model visibility.

2.3.2. Cellular Automata

Cellular automata is a modeling method based on raster data and is applied to physical systems and processes. It is a mathematical idealization of physical systems and an alternative to partial differential equations [45]. In the cellular automaton model, space and time are discrete, and the interaction only involves local combustible units. Therefore, based on cellular automata, a complex system can be described as a large number of locally interactive single units to realize the global behavior modeling of the system. Cellular automata describe how a single cell interacts with its neighbors during a simulation by defining a set of simple rules that describe the behavior of fire spread in global and spatial patterns as local neighbors as a result of the interaction between them [30].

Cellular automata can be identified by the geometry of regular cell arrangements, i.e., square or hexagonal cells in the two-dimensional case, and the need to consider the number of adjacent cells, such as four neighbors for a von Neumann neighborhood and eight for a Moore neighborhood in the area. Cellular automata models with square or regular hexagonal grids are widely used to simulate wildfire growth. At the same time, to simplify the calculation of the actual fire spread rate, it is usually assumed that the combustibles and terrain conditions in each cell are uniform, and the high-probability fire spread mode can also be determined by combining other empirical equations or local rules [3]. Each cell has a finite state with one or more variables and corresponding values. The transfer of heat and energy will define the state of the cell. At each time step, the cell needs to update the relationship between it and its neighbors. Interactions where the cell state changes according to a local transformation function applies to all cells in the scene [46].

Cellular automata have advantages in predicting macroscopic and complex dynamics. Because they use simple rules to define physical phenomena on a microscopic grid scale, the cellular automata model becomes effective for modeling involved forest fire spread behaviors. In some studies, cellular automata can also be easily further integrated with data from other sources, such as geographic information systems or local meteorological data, and applied to simulate fire spread to help firefighters identify fire suppression strategies and plan fire risk management policy [20].

For example, Wang et al. [12] analyzed the effects of combustibles, wind, temperature, and terrain to perform better simulations of forest fire spread in environments with different wind directions, different wind speeds, different terrain slopes, and different types of combustibles, ensuring that the model was accurate to forest fire dynamics simulations. Zheng et al. [47] proposed a new cellular automata modeling method by combining the extreme learning machine with the traditional forest fire CA framework, which effectively described the influence of wind speed on the fire spread pattern, thus achieving a more complex simulation of the forest fire spread mechanism. Mutthulakshmi et al. [48] considered the spatial spread of fire based on cellular automata. By predicting and analyzing the impact of fire intervention strategies on the spread of forest fires, they investigated fire protection strategies and deduced practical fire protection guidelines. M. Byari et al. [49] developed a suitable multi-scale CA modeling method based on 3D geometric units, which filled the gap in 2D modeling and further presented the complexity of modeling phenomena. In addition, Epaminondas Mastorakos et al. [50] and Dwi M J Purnomo et al. [51] used cellular automata to complete fire simulations. In addition, the simulations of Zhao et al. [52] on Australian forest fires, Sun et al. [53] on Amazon forest fires, and Mota et al. [54] on Portuguese forest fires were all implemented using cellular automata.

2.4. Interactive Fire Behavior

The plant model is the carrier of forest fire generation and extinguishment, so the interactive fire extinguishing behavior needs to be based on constructing plant models or forests. Research in this area has made a lot of progress in recent years; for example, Makowski et al. [55], Hädrich et al. [2] and Pałubicki et al. [56] implemented plant modeling with a custom method, while Li et al. [57] and Janoutová et al. [58] built plant models based on accurate information obtained from real-world images, point clouds, etc. In addition, one can further understand the processes that shape forest function, structure, and diversity by referring to recent forest model applications by Maréchaux et al. [59], which outline current ecologically essential topics. Then, after building a plant or forest model, one can further explore forest fire spread model design and implementation.

Choosing a forest fire spread model and reasonably expressing the spread of forest fires in a three-dimensional space can be used as the basis for studying fire extinguishing behavior. The purpose of realizing the design of interactive fire extinguishing behavior is to evaluate the range of fire attacks further, predict the evolution of the firefront, and simulate the impact of fire extinction at the forefront. In human-involved fire extinguishing, water can directly fight against the flame front boundary, so water is the most commonly used flame retardant, and water guns are the most widely used firefighting equipment for firefighters. Lu et al. [60] designed an interactive simulation water gun fire extinguishing training system based on virtual reality, which further saved fire training resources and increased the immersion and experience of virtual reality training. In addition to water guns, helicopters or UAVs are an effective way to extinguish fires. This is because helicopters hover, can move vertically, and have excellent maneuverability [19]. While UAVs are limited by cost and payload, their advantages of adapting to complex environments and effectively reducing casualties are undeniable, so they have also been further developed in fire protection [46].

At the same time, to train firefighters, Clifford et al. [61] used a multi-user, collaborative, multi-sensory (visual, auditory, tactile) virtual reality system to generate a realistic training environment for practicing aerial firefighting training scenarios, providing them with natural mental and physical stress to help aerial firefighters make quick, high-quality decisions.

3. Overview

In this paper, by studying the change rules and parameters in the process of forest fire spread, the potential rules between parameters are used to establish a related forest fire spread model, predict the trend of forest fire spread in natural scenes, and visualize this process in 3D virtual settings. Based on the cellular automata method, this research integrates static features such as fuel types and terrain features. It visualizes the influence of dynamic features such as weather factors on the cells, thereby simulating fire growth in grids representing natural forest landscapes according to weather scenarios. By modeling the plant model, the change in combustibles in different cells in the burning state is calculated, further expressing the material evolution of other plants during the spread of forest fires. This enhances the sense of reality and immersion in forest fires. In addition, based on building a forest fire spread model, this research explores the fire extinguishing principle. It explores how it affects the spread of forest fires by visualizing the fire extinguishing process of liquid flame retardants such as water guns, helicopter-dropped flame retardants, and simulated rainfall. The overall structure of this paper is shown in Figure 1.

4. Fire Spread Method

This chapter mainly introduces the research directed toward building a plant model library by assigning static and dynamic information to the cells, reducing the complexity and processing time of the algorithm while maintaining the correct fire spread behavior. Based on the principle of cellular automata, each cell in the scene is set as a different type of explosive (grass, tree), and the area where no cells are placed represents non-combustible terrain. In addition, the study further explored the fire extinguishing principle after constructing a forest fire spread model based on the principle of cellular automata. Since SpeedTree is a feasible tool for effectively creating digital plant assets, it is suitable for constructing plant models with different performances and styles and can provide maximum flexibility and work efficiency. Some examples of the plant model library constructed by it are shown in Figure 2.

4.1. The Principle of Forest Fire Spread Based on Cellular Automata

Generally in a two-dimensional scene, the cellular automata method uses square grids and regular hexagonal grids to neatly arrange them in rows and columns in the forest area, and its principle is shown in Figure 3 [47]. In the research on the three-dimensional world, the tree can be modeled into various shapes with the cellular automaton model: cone, cylinder, cylinder, and rectangle, etc. [22], so this research mainly uses different cells such as cuboid, sphere, and capsule to construct the plant. The interior of a cell cannot sensitively recognize and respond to changes in weather conditions, and each cell is considered a uniform material, but this is not real. In addition, cellular automata do not further consider complex behaviors such as reignition. Time t is an indispensable variable for realizing the simulation of the fire spread process based on cellular automata. Taking time t as the key effect parameter of fire spread, the factors affecting fire spread can be divided into dynamic factors and static factors [12]. Because weather factors change with time, weather-related weather factors are dynamic factors. The weather factors that affect the spread of forest fires include wind speed, temperature, and air humidity. Each factor not only affects the fire spread process individually, but also interacts. However, this complex interaction relationship is difficult to quantify. Therefore, this paper only considers the independent influence of weather factors on the fire spread process. Studies have shown that terrain has a significant impact on the fire spread process, and the terrain usually does not change during the spread of forest fires, so the factor related to terrain is static. This study mainly considers the impact of slopes on the spread of forest fires.

In addition, combustibles are the material basis of forest burning; their type and age as static factors do not change with the burning process, but the water content and quality of plants will change with the burning process. As the key factors that directly affect the spread speed of forest fires, there are mainly two types of cells in this paper. One is the cell representing grass, which can express surface fire, and the other is the cell representing a tree, which can express crown fire. The cells in the three-dimensional scene are not neatly arranged in rows and columns, but these two types of cells are placed in the scene with the distribution of the corresponding combustibles, as shown in Figure 4. The cellular automaton model is based on heterogeneous and discontinuous fuel-type grids, so to simplify the calculation of the basic fire spread rate, it is usually assumed that the combustibles and terrain conditions in each cell are uniform.

4.1.1. State Transition Rules

Simulating the spread of forest fires requires the design of simple transition rules between adjacent local units. This set of regulations can drive the state transfer of cells. This set of rules can only be applied when the cells are in the cell capture area, which means the unit cells may not necessarily be neatly arranged in a three-dimensional environment. The cell in this paper has four states in the process of forest fire spread: state 1—combustibles that have not been ignited; state 2—combustibles in the preheating state; state 3—combustibles that are burning; and state 4—combustibles burnt combustibles [47]. The state transition rules defined in this study are as follows:

Rule 1: If there is no neighboring cell in the burning state around the cell $C_i$ in state 1 at the discrete time step t, then the cell remains in state 1 at the next discrete time step $t+1$;

Rule 2: If there is a neighbor cell in the burning state around the cell $C_i$ in state 1 at the discrete time step t, then the cell is judged to maintain state 1 or enter state 2 at the next discrete time step $t+1$;

Rule 3: If the cell $C_i$ at the discrete time step t is in state 2, then the cell is judged to maintain state 2 or enter state 3 at the next discrete time step $t+1$;

Rule 4: If the cell at the discrete time step t$C_i$ is in state 3, then the cell will maintain state 3 or enter state 4 after calculation at the next discrete time step $t+1$;

Rule 5: If the cell $C_i$ in discrete time step t is in state 2 or state 3, fire extinguishing behavior or rainfall occurs, and then the cell enters state 3, 4, or returns to state 1 at the next discrete time step $t+1$ by calculating the temperature change. The state transition rules between adjacent local units designed in this paper are shown in Figure 5.

4.1.2. Fire Spread Rate

As a dynamic factor, weather factors have a major impact on forest fire spread, especially if the wind blowing in the direction of the flame spread directly increases the rate of forest fire spread [24]. Therefore, considering the main influencing factors such as fuel type, wind speed, humidity, and slope, the forest fire spread speed equation is as follows [62]:

$$R=R_0\ast K_{\phi }\ast K_{\theta }\ast K_S\ast K_r,$$

(1)

$$R_0=a\ast T+b\ast W+c\ast (100-RH)-d,$$

(2)

$$W=Int{\left(\frac{v}{0.836}\right)}^{\frac{2}{3}},$$

(3)

$$K_{\phi }=e^{0.1783\ast v\ast cos\phi },$$

(4)

$$K_{\theta }=e^{3.553\ast g\ast tan(1.2\ast \theta )}.$$

(5)

In the above equation, R is the forest fire spreading speed (m/min), $R_0$ is the forest fire spreading initial speed (m/min), $K_{\phi }$ is the wind correction coefficient, $K_{\theta }$ is the terrain correction coefficient, $K_S$ is the flammability index (can be obtained from the table) [62], $K_r$ is the time correction coefficient, a = 0.03, b = 0.05, c = 0.01, d = 0.3, T is the air temperature, W is the wind speed, RH is the air relative humidity, Int is the set integer, v is the wind speed (m/s), $\phi$ is the folder between the wind direction and the direction of fire spread angle, $\theta$ is the slope, and g is the aspect, 1 for uphill and −1 for downhill.

In addition, since the water content of combustibles will affect the initial speed of forest fire spread, the relationship between the water content of combustibles and the initial spreading speed of forest fires can be further modified into Equation (6) [63], in which m is the humidity of combustibles %:

$$R_1=1.0372\ast e^{-0.057\ast m}\ast R_0.$$

(6)

4.2. Principles of Fire Fighting Behavior

To further describe the principle of firefighting behavior, it is necessary to calculate the pyrolysis of wood to simulate the temperature change during the burning of forest fires to express the heat transfer during the pyrolysis of plants. Therefore, this paper realizes the pyrolysis process of forest plants by considering the temperature, water content, and mass loss rate [2], and uses liquid flame retardant water as a representative to explain the principle of fire extinguishing behavior.

1.

Temperature

$$\frac{dQ}{dt}=\lambda A\frac{\left(T_a-T_b\right)}{Hc}$$

(7)

The above equation calculates the heat absorbed by the tree module based on Fourier’s law, where the dimensionless carbon insulation parameters $Hc\in \left[0.01,0.1\right]$, and $\lambda$ is the thermal conductivity; the contact cross-sectional area between the trees is A; the temperature difference between the contact surfaces of two plants is $T_a-T_b$, and the unit is K. The elevated temperature $\Delta T$ can be calculated from the formula $\Delta T=\frac{Q}{cm}$ according to the heat Q, specific heat capacity c and lost mass m, and the unit is $°\mathrm{C}$.

2.

Water content

When the forest wood is in a state of heating or pyrolysis, the water inside the wood will gradually evaporate and vaporize. In a state of pyrolysis, it is necessary to consider the change in the water content of the plant caused by the newly generated water when the wood fiber decomposes; so, the water content of the wood can be described by Equation (8) as:

$${\frac{dw}{dt}=c}_{wm}\frac{dm}{dt}-\frac{\left(w-w_e\right)}{\tau },$$

(8)

where w is the current moisture content of the wood, $w_e$ is the equilibrium moisture content, $\tau$ is the time factor, and $\frac{dw}{dt}$ is the evaporated moisture mass. This equation can describe the drying process that exists before wood begins pyrolysis, indicating that $c_{wm}$ releases approximately $0.5362$ kg of water per kg of wood burned.

3.

Mass loss rate

The mass change rate $\frac{dm}{dt}$ can be described in Equation (9), which represents the variation of combustible materials during combustion. Both $H_c$ and A are partially dependent on the geometric shape of the tree and undergo changes during the combustion process, where $\alpha$ is a dimensionless coefficient to correct the reaction results, and $f_{T_M}$ represents the pyrolysis reaction rate defined as Equation (10) [2]:

$$\frac{dm}{dt}+\alpha f_{T_M}{H}_{c}A=0,$$

(9)

$$f_{T_M}=\eta \left(u\right)\ast \left\{\begin{array}{c}0,T_M\le T_0\hfill \\ S\left(\frac{\left(T_M-T_0\right)}{\left(T_1-T_0\right)}\right),T_0<T_M<T_1\hfill \\ 1,T_M\ge T_1\hfill \end{array}\right..$$

(10)

$$S\left(x\right)=3x^2-2x^3,$$

(11)

$$\eta \left(u\right)=\left({\eta }_{max}-1\right)S\left(\frac{u}{u_{ref}}\right)+1.$$

(12)

The function $S\left(x\right)$ describes an S-shaped curve that performs a smooth difference from 0 to 1 when the temperature is between $T_0=350°\mathrm{C}$ and $T_1=650°\mathrm{C}$; $\eta \left(u\right)$ is a function that expands the reaction rate by wind speed. When there is no wind, the corresponding output of the function is $\eta$ = 1, $u(x,t)$ is a time-dependent vector value describing the wind [2].

4.3. Liquid Flame Retardant

The effect of liquid flame retardants (take water as an example) on forest fires is that it absorbs heat, causing the plants in the pyrolysis process to not obtain enough heat to maintain the temperature, thereby reducing the temperature of the plants and causing the flames to be extinguished. When enough water participates in the process of forest fire spreading, the surface temperature of the plant will continue to cool down to be consistent with the ambient temperature. This process can be expressed in Equation (13), where the surface temperature of the plant can be expressed as $T_M\left(t\right)$, ${\alpha }_M$ is the diffusion coefficient, b is the temperature coefficient, and T is the ambient temperature:

$$\frac{\partial T_M}{\partial t}={\alpha }_M{\nabla }^2{T}_M+b\left(T-T_M\right)-\frac{\dot{Q}}{V_M{\rho }_M{c}_M}.$$

(13)

The cooling of the plant surface temperature by water depends on the heat transfer from the combustible surface to the covering water film and the amount of water. The water heat flux per unit area can be expressed in Equation (14), where $\stackrel{-}{c}=0.1{Wm}^{-2}{°\mathrm{C}}^{-1}$, $T_{sat}=100°\mathrm{C}$, and

$${\dot{q}}^{″}=\overline{c}{\left(T_M-T_{sat}\right)}^3.$$

(14)

The energy contained in vegetation with a volume of $V_M$ and a density of ${\rho }_M$ is $U_M$. Based on the specific heat capacity $c_M=2.5\mathrm{KJ}°{\mathrm{C}}^{-1}Kg$ and the absolute temperature ${T^{\prime }}_M$, Equation (15) can be obtained:

$$U_M=V_M{\rho }_M{{c_{M}T}^{\prime }}_M.$$

(15)

The rate of change in temperature for a given change in energy $U_M$ can be described in Equation (16), and the change in energy occurs through the heat transfer of $A_M$ on the plant surface:

$$\frac{d{T}_M}{dt}=\frac{d{U}_M}{dt}\frac{1}{V_M{\rho }_M{c}_M},$$

(16)

$$\frac{d{U}_M}{dt}={{\dot{q}}^{″}A}_M=\dot{Q}=\overline{c}{A}_M{\left(T_M-T_{sat}\right)}^3.$$

(17)

5. Algorithms Implementation

This chapter is mainly based on the above principles and methods. In the constructed virtual forest scene, two types of cells, grass and trees, are irregularly placed, and the forest fire spread algorithm is run to further realize the design of fire extinguishing behaviors.

Algorithm 1 Forest fire spread under the influence of dynamic factors

Input: Plants $\left\{T_1,T_2,\cdots ,T_n\right\}$, weather (wind speed, wind direction, air temperature, ambient relative humidity). Output: Status of all plants. 1: Obtain the initial state of all plants in Plants $T_1,T_2,\cdots ,T_n$, and obtain the weather; 2: for each $i=1,2,\cdots ,n$ do 3:     Update the surface temperature and water content of the $T_i$ according to the air temperature and the relative humidity of the environment, and adjust the deformation and offset of the $T_i$ according to the wind speed and wind direction; 4:     if $T_i$ in state 1 then 5:         if there are neighbors in state 3 around $T_i$ then 6:            Judging the transition of the $T_i$ state according to the changes in the $T_i$ properties (surface temperature, water content and mass) calculated by Equations (7)–(9); 7:         else if there are no neighbors in state 3 around $T_i$ then 8:            $T_i$ keep state 1; 9:         end if 10:     end if 11:     if $T_i$ in state 2 then 12:         if the current weather is rain then 13:            Judging the transition of the $T_i$ state according to the changes in the $T_i$ properties calculated by Equations (7)–(9) and (13); 14:         else if the current weather is not rain then 15:            Judging the transition of the $T_i$ state according to the changes in the $T_i$ properties calculated by Equations (7)–(9); 16:         end if 17:     end if 18:     if $T_i$ in state 3 then 19:         if the current weather is rain then 20:            Judging the transition of the $T_i$ state according to the changes in the $T_i$ properties calculated by Equations (7)–(9) and (13); 21:         else if the current weather is not rain then 22:            Judging the transition of the $T_i$ state according to the changes in the $T_i$ properties calculated by Equations (7)–(9); 23:         end if 24:     end if 25:     if $T_i$ in state 4 then 26:         Remove $T_i$ from Plants until the application ends and returns to the initial state 27:     end if 28:     Update the forest fire spread speed according to Equation (1); 29: end for 30: Get the termination status of all plants in Plants.

When the ignition is successful, the combustion message will be captured between adjacent local cells, and the cells will judge their state according to the state transition rules to realize the spread or obstruction of a forest fire in the forest scene.

This study uses Unity as a tool for application development and uses C# language to implement related functions, logical designs, and calculations. Plants $\left\{T_1,T_2,\cdots ,T_n\right\}$ represent the cells contained in all plants in the forest. Algorithm 1 mainly introduces the influence of dynamic factors (wind force, wind direction, precipitation, etc.), using plants that are in state 2 or 3. These fire extinguishing behaviors will affect the process of forest fire spread. Therefore, when the liquid flame retardant participates in the fire extinguishing process, the related calculation is similar to that in Algorithm 1 when the weather is rainy.

6. Results and Discussion

This paper builds a forest fire spread algorithm based on cellular automata and further realizes the visualization of the forest fire spread process in the three-dimensional world by considering the impact of static and dynamic factors. Therefore, this chapter will describe the results of the algorithm in the previous chapter. The simulation results are discussed and analyzed. This research mainly selects the weather scene after constructing the forest terrain and records the state of the cell and the transfer of the state. By repeating this process many times, the result of forest fire spread is obtained, as shown in Figure 6.

6.1. Forest Fire Spread

Since combustibles, terrain, and weather factors are essential factors affecting the spread of forest fires, to discuss the relevant simulation results, this study first considered the flame spread behavior in a homogeneous medium under no wind conditions, as shown in Figure 7. On flat terrain and without the influence of dynamic factors such as wind and precipitation, if a fire is ignited somewhere in the terrain and spreads for a while, it can be found that the flame spread area is approximately circular, which is consistent with the results of Wang Xuehua et al. [12].

For terrain conditions, altitude, slope, and slope aspect are essential factors that affect forest fire spread because the distance between the highest altitude and the lowest altitude in the terrain that simulates forest fire spread is usually tiny. Therefore, the study mainly considered the influence of slope and aspect on the spread of forest fire. Under flat and windless conditions, two areas with the same uniform medium have different slopes, and the two terrains are ignited at the corresponding cells. The results show that the spread of the flame is accelerated by the slope, as shown in Figure 8.

Wind speed and wind direction greatly influence forest fire spread, and the forest fire spread model simulated the relevant results after considering this critical factor. In a homogeneous medium, regardless of the influence of slope, the impact of wind direction on the flame spread is shown in Figure 9, and the power of different wind forces on the flame spread is also different, as shown in Figure 10. The results show that higher wind speeds lead to a more rapid spread of forest fires, resulting in significant changes in burned areas between individual time steps.

Since the forest is composed of many types of plants, to realize the simulation of heterogeneous fuel combustion, this study discovered the transition from surface fire to crown fire, as shown in Figure 11. Figure 6 shows the spread of forest fires in heterogeneous combustibles under non-flat terrain and windy conditions, the flame spread achieved by Cristobal et al. [3] in a two-dimensional scene, and the transition from surface fires to forest fires realized by K.A.M et al. [22] in Figure 12. The visual expression of forest fire spread behavior in the 3D scene implemented in this article is more realistic and can provide an immersive experience compared to the relevant terms in the above research [3,22].

6.2. Fire Fighting Behavior

Since the water bombing behavior can be carried out near the front line of flame propagation, forest fire fighting behavior usually uses the aerial water bombardment of burning plants, and the fire line generated by it is used to limit the spread of forest fires further. Therefore, the study realized the helicopter tossing water in the 3D scene’s fire extinguishing behavior, as shown in Figure 13. Compared with Han Yangnanbing et al. [19], who explored the physical laws of helicopters dripping water, this study pays more attention to the real-time performance and accuracy of the visualization method, which improves the sense of reality and immersion in the virtual environment.

Of course, in daily training and actual combat, firefighters often use water guns to extinguish fires. Water guns have a certain flexibility and are cheaper to operate than helicopters. Therefore, this research has also realized water gun fire extinguishing behavior, as shown in Figure 14. In addition, compared with water guns and helicopter firefighting, rainfall has a broader range of forest fire spread, as shown in Figure 15.

6.3. Summary

Forest fire spread and firefighting behavior are very complex. By exploring the influence of static and dynamic factors on forest fire spread, this study constructed a three-dimensional virtual forest scene and selected the weather to realize the dynamic simulation of forest fire spread behavior, strengthening this realism and immersion in the process. Based on the simulation of forest fire spread, fire-fighting behaviors such as water guns, helicopter-sprayed water, and rainfall fire extinguishing are realized, and the relationship between the characteristics of forest fire behavior and fire fighting behavior is further expressed.

7. Conclusions and Outlook

In order to realize the virtual simulation of a forest fire and seek to reproduce the occurrence–spread–extinguishment of a forest fire in a three-dimensional environment, this study proposes a lightweight fire spread model. The main conclusions are as follows:

(1)

This research mainly establishes a fire spread model based on cellular automata, comprehensively considering static and dynamic factors such as combustibles, terrain, weather, etc., to realize the visualization of flame spread behavior in 3D virtual forest scenes. Slope, wind direction, and wind speed are the main dynamic factors that determine the direction and speed of forest fire spread, while rainfall will hinder the spread of fire;

(2)

Research-designed grass and tree cells can express the types of combustibles and the simple conversion rules between adjacent local cells to drive cell state transitions to achieve the spread and expansion of forest fires. This further simplifies calculations between cells, thereby speeding up simulation efficiency;

(3)

Preliminary exploration of fire extinguishing behavior (water gun spraying and helicopter firefighting) was conducted. During the flame burning process, by showing the change in plant material, the realism and immersion of forest fire spread were improved. This shows that water has application advantages as a liquid flame retardant, which can effectively prevent the spread of flames.

Of course, the study has some limitations:

(1)

High time-frequency meteorology is needed to improve the accuracy of forest fire spread simulations. The data ensure that dynamic factors are updated in a timely manner and give more details about the spread of fire. Therefore, research can obtain more forest fire spread details by coupling large-scale forest fires with the climate system, and based on their interactions, these spread details can help decision makers make reasonable fire suppression plans.

(2)

Due to the generality of the model constructed in this study, although this study can reproduce the observed final fire boundary, the model cannot express the uniqueness of fire behavior because it has not been verified by a large number of fire samples; these include behaviors such as deflagration, re-ignition etc. Therefore, to improve the model’s accuracy and analyze the factors that lead to forest fires, follow-up research can optimize the model by analyzing more fire samples and using machine learning methods. It is important to further explore the influence of the law of forest fire behavior, to ensure the reliability and rationality of the model.

(3)

Since the process of forest fire spread is very complicated, there are many factors that affect the spread speed of forest fires. Therefore, in addition to the factors involved in this paper, the influence of other factors on fire spread needs further study. For example, the situation where sparks from burning combustibles can cause a fire to spread is not taken into account.

Based on the above discussion, the next step of this study is to strengthen the logical design of fire extinguishing visualization so as to build a complete forest fire occurrence–decision–fire extinguishing system. The optimal allocation of fire extinguishing resources in forest fire areas can be achieved, and visual decision support can be successfully provided for forest fire rescue commands, fire disaster assessment, and fire recovery.