# Mathematical models for estimate of the ecological consequences of the impact of the pyrogenic factor on forest ecosystems

Keywords: mathematical model, forest fire, combustion parameters, fire intensity classification

### Abstract

There is a need for the development of simple analytical mathematical models of the burning of large forest areas, necessary for the assessment of the ecological consequences of the impact of the pyrogenic factor.

Purpose. Develop mathematical models describing the spread of large-scale forest fires aimed at estimate the ecological consequences of the impact of the pyrogenic factor.

Methods. Analytical review of research on the problem, theoretical and computational, mathematical modeling.

Results. The results of the main parameters analysis of large forest areas combustion are presented. These include the area covered by the fire, the duration of the fire, the burnout time, the specific mass of combustible materials, the energy and power of combustion, the specific calorific value, the intensity of combustion, the movement speed of the combustion front, the influx of combustible materials, etc. Simple analytical mathematical models of large forest areas combustion have been established. These include the following models: a model with a constant growth rate of the fire area, a two-dimensional model, a model with sectorial movement of the combustion front, a model with a linear growth of the length of the combustion front, a model with a quadratic growth of the change rate of the fire area, and a generalized model. A new fire intensity classification has been proposed, containing 1–7 points from extremely low to extreme intensity. The maximum area covered by the fire (10–100 thousand km2), combustion energy (1–10 EJ) and combustion power (0.1–1 PW) have been estimated.

Conclusions. Simple analytical mathematical models of the combustion process of large forest surface areas, which are necessary for quantitative assessment of the ecological consequences of fires, have been developed.

### Author Biographies

L. F. Chernogor, V. N. Karazin Kharkiv National University, 4, Svobody Sqr., 61022, Kharkiv, Ukraine

DSc (Physics and Mathematics), Prof., Head of the Department of Space Radio Physics

A. N. Nekos, V. N. Karazin Kharkiv National University, 6, Svobody Sqr., 61022, Kharkiv, Ukraine

DSc (Geography), Prof., Head of the Department of Environmental Safety and Environmental Education

G. V. Titenko , V. N. Karazin Kharkiv National University, 6, Svobody Sqr., 61022, Kharkiv, Ukraine

PhD (Geography), Head of Karazin Institute of Environmental Sciences

L. L. Chornohor , V. N. Karazin Kharkiv National University, 6, Svobody Sqr., 61022, Kharkiv, Ukraine

Student of Karazin Institute of Environmental Sciences

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Published
2022-11-25
How to Cite
Chernogor, L. F., Nekos, A. N., Titenko , G. V., & Chornohor , L. L. (2022). Mathematical models for estimate of the ecological consequences of the impact of the pyrogenic factor on forest ecosystems. Visnyk of V. N. Karazin Kharkiv National University Series «Еcоlogy», (27), 51-62. https://doi.org/10.26565/1992-4259-2022-27-04
Section
Environmental ecological safety

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