Study on Forest Fire spread Model of Multi-dimensional Cellular Automata based on Rothermel Speed Formula

Zhang, Shiyu; Liu, Jiuqing; Gao, Hewei; Chen, Xiandong; Li, Xingdong; Hua, Jun

doi:10.1590/01047760202127012932

ABSTRACT

Background:

The spread of forest fire is a complex natural phenomenon. The cellular automata(CA) is a common model of forest fire spread, which fails to combine the unique combustion properties of forest fire spreading, resulting in inaccurate simulation results. In order to improve the accuracy of forest fire spread simulation, the Rothermel forest fire rate formula is simplified and combined with CA to form a multi-dimensional cellular automata(MD-CA) model of forest fire spread with different combustion properties in each cell. The formulas of the spread rate of forest fire in eight directions are obtained through the training datasets, and the testing datasets are used to compare the simulation results of CA model, MD-CA model and the actual fire spread.

Results:

It is concluded that the simulated areas and perimeters of the MD-CA are closer to the actual forest fire spread, the area error rate is 9.42% - 15.63%, and the perimeter error is 4.21% - 8.99%, The errors are less than CA model.

Conclusion:

The MD-CA model based on Rothermel has the strong ability to simulate the spread of fire in the laboratory, however, how to eliminate the errors over time is the task of the next stage.

Keywords:
Rothermel; cellular automata; forest fire spread; fire contour area and perimeter; error rate

HIGHLIGHTS

The complex Rothermel formula is simplified to better adapt to cellular automata.

The forest fire spread model of multi-dimensional cellular automata combines slope, moisture content, wind speed and other factors.

Multi-dimensional cellular automata has a better effect of spreading simulation.

It provides a new method for the development of forest fire spread model.

[1] ✤ lixd@nefu.edu.cn

Num	Mass (kg)	Area (m²)	Load capacity (kg.m^-2)	Bed thickness (m)	Slope direction/ inclination	Moisture content	Angle between wind direction and spread direction
1	0.69	0.8*0.6	1.44	0.05	Up/8°	5.24%	0°
2	0.62	0.8*0.6	1.29	0.04	Up /8°	6.14%	45°
3	0.83	0.8*0.6	1.73	0.07	Up /8°	7.00%	90°
4	0.91	0.8*0.6	1.90	0.07	Up /8°	8.37%	135°
5	0.63	0.8*0.6	1.31	0.06	Up /8°	8.37%	180°
6	0.93	0.8*0.6	1.93	0.07	Down/8°	8.92%	0°
7	0.53	0.8*0.6	1.10	0.05	Down/8°	8.92%	45°
8	0.55	0.8*0.6	1.14	0.05	Down/8°	8.81%	90°
9	1.09	0.8*0.6	2.26	0.08	Down/8°	6.49%	135°
10	0.73	0.8*0.6	1.52	0.05	Down/8°	8.81%	180°
11	1.01	0.8*0.6	2.10	0.08	Flat/0°	5.24%	0°
12	0.79	0.8*0.6	1.65	0.04	Flat /0°	6.14%	45°
13	0.92	0.8*0.6	1.92	0.07	Flat /0°	6.45%	90°
14	0.80	0.8*0.6	1.67	0.05	Flat /0°	5.10%	135°
15	0.98	0.8*0.6	2.05	0.07	Flat /0°	5.10%	180°

Num	Slope direction/ inclination	Wind direction	Surface area of the first stage (m²)	Surface area of the second stage(m²)	Load capacity (kg.m^-2)	Bed thickness (m)	Moisture content
1	Flat-Up/8°	Downwind	0.8*0.5	0.8*0.5	2.28	0.05	7.68%
2	Up-Down/8°	Headwind	0.8*0.5	0.8*0.5	1.82	0.05	5.38%

Slope direction/inclination	Angle between wind direction and spread direction	B	C	E	G	H	I	J	K
Up/8°	0°	34.06	8.20	-21.18	7207	0.192	6520	434656	0.01
Up /8°	45°	32.14	8.67	-20.08	7020	0.215	6014	424532	0.01
Up /8°	90°	36.34	8.90	-28.77	7819	0.216	6732	420410	0.01
Up /8°	135°	33.11	8.61	-20.84	7863	0.205	6240	474322	0.01
Up /8°	180°	31.75	8.23	-24.19	7014	0.230	6241	417772	0.02
Down/8°	0°	32.89	8.65	-29.77	7426	0.238	6127	415210	0.03
Down/8°	45°	31.17	8.64	-25.12	7262	0.258	6002	414984	0.04
Down/8°	90°	36.74	8.78	-23.99	7102	0.212	6011	431741	0.03
Down/8°	135°	31.03	8.87	-23.45	7017	0.210	6280	435599	0.03
Down/8°	180°	34.99	8.86	-23.92	7105	0.282	6072	420795	0.01
Flat/0°	0°	30.41	8.17	-24.76	7001	0.247	6046	-	0.01
Flat/0°	45°	34.14	8.56	-24.63	7124	0.222	6009	-	0.02
Flat/0°	90°	30.06	8.17	-20.54	7418	0.200	6291	-	0.02
Flat/0°	135°	34.84	8.46	-21.89	7012	0.209	6031	-	0.01
Flat/0°	180°	37.54	8.85	-21.68	7004	0.237	6008	-	0.01

Time	Tesing dataset 1				Tesing dataset 2
	CA			Multi-dimensional CA			CA		Multi-dimensional CA
	Area	Perimeter	Area	Perimeter	Area	Perimeter	Area	Perimeter
11	11.18%	9.99%	9.42%	4.21%	11.36%	10.59%	10.27%	5.14%
21	12.69%	10.54%	11.64%	4.74%	12.24%	11.07%	11.85%	5.98%
31	14.12%	10.65%	12.04%	5.22%	13.73%	12.29%	12.07%	6.49%
41	15.80%	12.36%	12.41%	6.22%	14.83%	12.76%	12.21%	6.94%
51	16.05%	13.29%	13.97%	6.81%	16.09%	13.23%	13.42%	7.35%
61	17.08%	13.68%	14.06%	7.44%	17.80%	14.19%	14.33%	8.09%
71	20.64%	14.14%	14.33%	8.74%	19.21%	14.80%	15.16%	8.25%
81	—	—	—	—	21.17%	15.20%	15.63%	8.99%
Average	15.37%	12.09%	12.55%	6.20%	15.80%	13.01%	13.12%	7.15%