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Valery Akimov, Maxim Bedilo, Olga Derendiaeva RT&A, No 4 (76)
MODELS FOR FORECASTING EMERGENCIES Volume 18, December 2023
STATISTICAL MODELS FOR FORECASTING NATURAL
EMERGENCIES
Valery Akimov, Maxim Bedilo, Olga Derendiaeva
All-Russian Research Institute for Civil Defense and Emergencies of the Ministry of Emergency
Situations of Russia akimov@vniigochs. ru
Abstract
The article considers predictive-analytical solutions for natural hazards for urbanized areas, the mathematical basis of which is Bayesian classifiers. The result of the work is a formalized description of models for predicting forest fires, the consequences of earthquakes and floods resulting from floods.
Keywords: predictive and analytical solutions; Bayes method; emergency situations of a natural nature; Forest fires; earthquakes; floods.
I. Introduction
The subject of the study is natural hazards for urban areas with the aim of their formalized description using Bayesian classifiers. The main part of the work contains three sections: a model for predicting forest fires; model for predicting the consequences of earthquakes; model for forecasting floods due to floods.
II. Methods
Statistical Model for Forest Fire Prediction. As part of the creation of the hardware-software complex "Safe City", an approach to modeling forest fires (hereinafter referred to as LP) is proposed, which is based on Bayesian methods [1]. In the statistical model for predicting the LP, the following parameters are subject to probabilistic assessment using a Bayesian classifier: speed of the riding LP; area and speed of the downstream LP [2]. The calculation of the average speed of the front of the upper LP for various gradations of wind speed is calculated by the equation:
^frsr
1 vfri
Ni
(1)
Where:
j is the range of wind speed values corresponding to the j-th gradation (according to Table 1);
Valery Akimov, Maxim Bedilo, Olga Derendiaeva RT&A, No 4 (76) MODELS FOR FORECASTING EMERGENCIES_Volume 18, December 2023
Nj is the number of upper LPs recorded at wind speeds that are in the detected values,
detection of the j-th gradation, units;
vfri is the front speed of the i-th riding LP, m/min.
Table 1: Directory of gradations of wind speed values
№ Range of values, m/s
1. Less than 0,3
2. [0,3; 1,6)
3. [1,6; 3,4)
4. [3,4; 5,5)
5. [5,5; 8)
6. [8; 10,8)
7. [10,8; 13,9)
8. [13,9; 17,2)
9. [17,2; 20,8)
10. [20,8; 24,5)
11. [24,5; 28,5)
12. [28,5; 32,7)
13. from 32,7 and more
The main indicators of the propagation of low-level LPs are calculated according to the Rothermel model, which is based on the position that the flame propagation speed is proportional to the ratio of the heat of combustion of the material to the heat of heating new portions of combustible material to the ignition temperature [3].
Determining the speed of the propagation front of the grassroots LP in this model is carried out as follows.
According to the data obtained from the results of collecting the characteristics of the forest area, the composition of the forest combustible material (FCM) for this area is determined, after which the surface area per 1 m2 of the territory is determined for each layer of the FCM according to the formula:
aiM0i
A'=— (1)
Where:
M0 is the average reserve of the layer of forest materials, kg/m2; ct is the specific surface area of the FCM layer, m-1; p is the density of the LCM layer, kg/m3.
The values of the parameters of formula (2) are determined according to table 2.
Table 2: Average characteristics of the ground cover
Compound Designation Lichen Moss schreber Nee dles Dry Leaves cereal s Bush Logging waste
Average stock of a layer of LCM, kg/m2 1,7 1,0 0,3 0,15 0,225 0,9
Specific surface area of the LCM layer, m-1 a 2000 2500 6000 11560 18170 6560 4920
Valery Akimov, Maxim Bedilo, Olga Derendiaeva MODELS FOR FORECASTING EMERGENCIES RT&A, No 4 (76) Volume 18, December 2023
Heat of
combustion, h 4300 4700 4500 4880 4200 4400
kcal/kg
Density LGM layer, kg/m3 P 300 512 460 420 512
Layer height, m S 0,12 0,1 0,075 0,5 0,6 0,7
Critical moisture content, kg/kg Mx 0,3 0,5 0,3 0,4 0,2
The total surface area (AT) of all LCM layers is calculated by the formula:
n
a7
(3)
¿=1
Next, the wind speed is calculated at a level of 6 meters above the crowns of the forest stand (WZ6) according to the formula:
= Wzlo
Zrf + 6
10
(4)
Where:
WZ10 - wind speed according to the nearest weather station; Zd is the average stand height. Then the speed of propagation of the fire front in the absence of wind and slope (vfr) can be calculated by the formula:
0,048hsrVsUosrVrn.r$ ._.
(5)
vo vfr
(Psr + PSrST)QY£aSr
0,28
Where:
r]s is a coefficient that takes into account the mineral composition of forest fuels (assumed to be 0.42);
SR - mineral content.
Based on the assumption that the lower LP in a homogeneous medium propagates in an ellipse,
the area of the LP can be determined as follows.
First, the ratio of the length of the LP to its width (LB) is determined by the formula:
LB = 0,936 exp(0,2566W) + 0,461 exp(-0,1548W) - 0,397. (6)
Next, the ratio of the leading edge of the LA to its trailing edge (HB) is determined by the formula:
LB + VLB2 - 1
HB=--. (7)
LB - VLB2 - 1
The values a, b and c are calculated by the formulas:
vfr(1 +HB)
b = frv , (8) 2 HB ,
Valery Akimov, Maxim Bedilo, Olga Derendiaeva RT&A, No 4 (76) MODELS FOR FORECASTING EMERGENCIES_Volume 18, December 2023
' = * ■ (9)
vfr
c=b-m. (10)
The final value of a, b and c is determined by multiplying each of the given values by the forecast period in minutes.
Then the LP area (Sip) is calculated by the formula:
Sip = nab. (11)
Statistical model for predicting the consequences of earthquakes
The model for predicting the consequences of earthquakes is based on calculation methods for assessing the parameters of seismic impact, determining the degree of destruction of buildings and structures, elements of urban infrastructure, including theoretical approaches in the field of statistical data analysis based on the Bayesian method of interpreting probability.
The main initial data for the formation of the basic training set of the model for predicting the consequences of earthquakes are the following groups of parameters: characteristics of earthquakes; characteristics of damage to buildings and structures during earthquakes; characteristics of buildings and structures; characteristics of territories; parameters of the meteorological situation [4].
At the stage of training the model, the parameters of the hypotheses are determined based on the values of the parameter "Degree of damage to the building (structure)".
After training, the process of predicting events corresponding to hypotheses begins on new values of the observed parameters.
The order of collecting new values of the observed input data and processing them corresponds to similar processes when training the model, except that the parameters of the hypotheses (estimating the posterior probabilities of the hypotheses) are determined by the Bayesian classifier.
When forecasting using this model, each building or structure is considered separately. For these purposes, the characteristics of all buildings and structures in the controlled area are prepared in advance [5].
Statistical model for flood forecasting
The main input data for the formation of the base training set of the model for flood forecasting due to floods are flood data due to heavy rainfall floods; data characterizing sections of rivers with sections of their watersheds; data characterizing the watersheds of the observed sections of the rivers; data characterizing water management systems in the observed sections of rivers; data characterizing controlled settlements (hereinafter referred to as CPs) located in areas of probable flooding of the area; data characterizing the hydrological situation in river sections; data characterizing the meteorological situation in the observed areas of the terrain; data characterizing the prevailing landscape of the area, the types and composition of soils within the boundaries of the NP and the catchment areas of the observed rivers [6].
In this model, the most significant indicators are the calculated hydromorphological parameters during the flood period.
When determining the calculated hydromorphological characteristics of river points, the
Valery Akimov, Maxim Bedilo, Olga Derendiaeva MODELS FOR FORECASTING EMERGENCIES
RT&A, No 4 (76) Volume 18, December 2023
following calculation methods are used [7]:
in the presence of data from hydrometric observations - directly from these data;
in case of insufficiency of hydrometric observation data, by reducing them to a multi-year period according to the data of analogue rivers with longer observation series;
in the absence of hydrometric observation data and the impossibility of comparison with the given analogous rivers, according to calculation formulas using maps based on the totality of observational data from the entire network of monitoring points for the hydrological situation in the corresponding area or a larger territory.
III. Results
Thus, this article considers predictive and analytical solutions for natural hazards for urban areas, the mathematical basis of which is Bayesian classifiers. The result of the work is a formalized description of models for predicting forest fires, the consequences of earthquakes and floods resulting from floods.
IV. Discussion
The discussion of the verbal and mathematical foundations of predictive modeling of natural emergencies is quite active in the scientific literature [8 - 10].
The scientific novelty of the developed models lies in a single scientific approach to their creation, namely, the use of a statistical processing method based on Bayes' theorem.
Bayesian probability is currently developing as the main method of forecasting in terms of building and training neural networks, in contrast to frequency probability - when the probability is determined by the relative frequency of occurrence of a random event with sufficiently long observations.
For scientific forecasting of crisis situations and incidents using the Bayesian method and Bayesian networks, a large amount of up-to-date data is required for modeling natural disasters, which is typical for often recurring negative events.
Due to the lack of statistical data, Bayesian methods are not applicable for predicting catastrophic natural disasters that occur rarely, but with significant damage.
References
[1] Predictive and analytical solutions for natural, man-made and biological and social threats of a unified system of information and analytical support for the safety of the environment and public order "Safe City" / V. A. Akimov, A. V. Mishurny, O. V. Yakimyuk [and etc.]. - Moscow: All-Russian Research Institute for Civil Defense and Emergency Situations of the Ministry of Emergency Situations of Russia, 2022. - 315 p. - ISBN 978-5-93970-278-2. - EDN MGXNYI.
[2] Akimov, V. A. Large natural fires as sources of natural emergencies / V. A. Akimov, M. V. Bedilo, E. O. Ivanova // Civil Security Technologies. - 2022. - T. 19, No. 2 (72). - S. 11-13. - DOI 10.54234/CST.19968493.2022.19.2.72.2.11. - EDN PGJCMG.
[3] Barovik, D. V. Computer model, examples of the analysis of the spread of ground fires / D.V. Barovik, V. B. Taranchuk // Problems of physics, mathematics and technology. - 2020. - No. 4 (45). - S. 113-120. - EDN DIJSBZ.
[4] Akimov, V. A. Hazardous geophysical phenomena and processes as sources of natural emergencies: a model of medium-term earthquake forecasting / V. A. Akimov, M. V. Bedilo, E. O. Ivanova // Civil Security Technologies. - 2022. - T. 19, No. 1 (71). - S. 20-23. - DOI 10.54234/CST.19968493.2022.19.1.71.4.20. - EDN QICTLF.
Valery Akimov, Maxim Bedilo, Olga Derendiaeva MODELS FOR FORECASTING EMERGENCIES
RT&A, No 4 (76) Volume 18, December 2023
[5] Preliminary national standard of the Russian Federation PNST 763-2022 "Safety in emergency situations. Safe city. Earthquake forecasting. General requirements".
[6] Akimov, V. A. Hazardous hydrological phenomena and processes as sources of natural emergencies: a verbal model / V. A. Akimov, M. V. Bedilo, S. P. Sushchev // Civil Security Technologies. - 2021. - T. 18, No. 4 (70). - P. 4-8. - DOI 10.54234/CST.19968493.2021.18.4.70.1.4.
- EDN EVUUFA.
[7] Security of Russia. Legal, socio-economic and scientific and technical aspects. Analysis and provision of security from emergency situations / V. A. Akimov, A. A. Antyukhov, E. V. Arefieva [and others]; Security Council of the Russian Federation, Russian Academy of Sciences, EMERCOM of Russia, Rostekhnadzor, Russian Science Foundation, Rostec State Corporation, Rosatom State Corporation, Rosneft Oil Company PJSC, Russian Railways OJSC, Transneft PJSC, Gazprom PJSC. - Moscow: MGOF "Knowledge", 2021. - 500 p. - ISBN 978-5-87633-199-1. - EDN FXIJPZ.
[8] Akimov, V. A. Classical and post-non-classical methods for predicting natural emergencies / V. A. Akimov, M. V. Bedilo // Civil defense on guard of peace and security: Proceedings of the VII International scientific and practical conference dedicated to the World Day of Civil Defense in the year of the 90th anniversary of the formation of the Academy of the State Fire Service of the Ministry of Emergency Situations of Russia. At 5 a.m., Moscow, March 01, 2023. Volume Part I. -Moscow: Academy of the State Fire Service of the Ministry of the Russian Federation for Civil Defense, Emergencies and Disaster Relief, 2023. - P. 20-27. - EDN YAVGTG.
[9] Akimov, V. A. Scientific forecasting of natural emergencies / V. A. Akimov, E. O. Ivanova // Russia in the XXI century in the context of global challenges: problems of risk management and security of socio-economic and social political systems and natural-technogenic complexes: collection of materials of the All-Russian Scientific and Practical Conference, Moscow, April 26-27, 2022 / Russian Academy of Sciences, International Independent Environmental and Political University, State University of Management. Volume Issue 1. - Moscow: State University of Management, 2022. - P. 114-119. - EDNFFDBHY.
[10] Akimov, V. A. Modern methods of studying emergency situations of natural, technogenic and biological and social nature / V. A. Akimov, M. V. Bedilo // Civil defense on guard of peace and security: Materials of the VI International scientific and practical conference dedicated to World Civil Defense Day. In 4 parts, Moscow, March 01, 2022 / Comp. V.S. Butko, M.V. Aleshkov, S.V. Podkosov, A.G. Zavorotny [i dr.]. Volume Part I. - Moscow: Academy of the State Fire Service of the Ministry of the Russian Federation for Civil Defense, Emergencies and Disaster Relief, 2022. - P. 16-24. - EDN HSSYVB.
