=Paper= {{Paper |id=Vol-1839/MIT2016-p01 |storemode=property |title= GIS-technologies and mathematical simulation as tools for lightning-caused forest fire danger prediction |pdfUrl=https://ceur-ws.org/Vol-1839/MIT2016-p01.pdf |volume=Vol-1839 |authors=Nikolay Baranovskiy,Vladimir Barakhnin,Elena Yankovich }} == GIS-technologies and mathematical simulation as tools for lightning-caused forest fire danger prediction== https://ceur-ws.org/Vol-1839/MIT2016-p01.pdf

Mathematical and Information Technologies, MIT-2016 — Information technologies

GIS-Technologies and Mathematical Simulation
as Tools for Lightning-Caused Forest Fire
Danger Prediction

Nikolay Baranovskiy1 , Vladimir Barakhnin2,3 , and Elena Yankovich1
1
National Research Tomsk Polytechnic University,
Lenina ave. 30, 634050 Tomsk, Russia
2
Novosibirsk State University, Pirogov st. 2, 630090 Novosibirsk, Russia
3
Institute of Computational Technologies SB RAS,
Lavrent’yev ave. 6, 630090 Novosibirsk, Russia
firedanger@narod.ru

Abstract. New approach to forecasting of forest fire danger caused by
storm activity is presented in the article. This approach is based on us-
ing the criteria of forest fire danger and physically proved mathematical
models of forest fuel ignition. The formula of criterion is based on a
probabilistic assessment of forest fire danger and uses the main theo-
rems of probability theory. Data of a forest fire retrospective on the con-
trolled territory are used to assess the members in probabilistic criterion.
Timiryazevskiy local forestry of the Timiryazevskiy timber enterprise of
the Tomsk region is considered as a typical territory. It is shown that
it is not enough to use only statistical information on forest fires for an
adequate assessment of the forest fire danger caused by action of storm
activity. Visualization of data is carried out with the use of geoinforma-
tion technologies.

Keywords: GIS, mathematical simulation, forest fire danger, predic-
tion, lightning.

1 Introduction
The remote areas of forested territories are characterized by a big share of the
forest fires caused by action of storm activity [1]. The great value of the area
passed by fire is noted for such fires [2]. Such fires in the forests are detected
with delay when the ignition center already reached the big sizes. It is either
impossible or ineffective to suppress ignitions in taiga zone. Fire fades in case
of the beginning of long rains, or at burning out of all forest area before fire
came across the natural barrier (for example, river). In such a situation, the
most perspective approach is to forecast the forest fire danger and to carry out
preventive measures in controlled forested territories [3]. There are various forest
fire danger forecast systems taking into account storm activity developed in the
different countries of the world [4–6]. However, all these systems have no physical
basis and are based mainly on the analysis of statistical information on forest
fires and characteristics of the forested territory [7].

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Mathematical and Information Technologies, MIT-2016 — Information technologies

2 Background
Storm discharges are one of the reasons for forest fires. Lightning is an electric
discharge conditioned by the division into positive and negative discharges in
the clouds that leads to a difference in potentials of the range 10-100 mV [8].
In order for the division into discharges to happen, it is necessary that water be
present in all three phases solid, liquid and gas [9].
According to the development conditions, storms are divided into the air-
mass and frontal ones. Air-mass storms over a continent occur as the result of
the local air heating from the ground surface that leads to a development of
rising flows of the local convection and to a formation of heavy cumulonimbus
clouds in it. The frontal storms occur on the borders of warm and cold air
masses [10]. There may be the cloud-to-cloud and cloud-to-ground discharges.
Around 90% of cloud-to-ground discharges are negative, and the nature of the
remaining 10% of positive discharges is not fully clear [11]. The cloud-to-ground
discharges, i.e. ground storm discharges, can cause forest fires [12]. The energy
characteristics for positive and negative ground storm discharges are different,
and these differences are substantial in terms of igniting the forest fuels. Due to
the vast majority of positive discharges, all the energy reaches the surface in one
stroke, and a multi-stroke is typical for the negative discharges [13].
Wide statistics on ground storm discharges has been collected within the
functioning of the US National Lightning Detection Network [14]. This system
may identify most ground storm discharges on USA and Canada territories with
the spatial resolution of several kilometers and determination accuracy in time
of 1 msec. Due to the system operation, the data on the stroke polarity, stroke
peak current and stroke complexity are archived (if it is a single or multi-stroke)
[13].
In Russia, between 1992 and 2000, storm-induced forest fires equaled 37 to
53 % of the area where fire had spread, with a relative number of 8.817.5 % [15].
Dry storms, producing mass ignitions on large spaces, often create a very intense
situation [16].
Canadian Forest Fire Danger Rating System (CFFDRS) has two main sub-
systems (modules) Canadian Forest Fire Weather Index (FWI) System and
Canadian Forest Fire Behavior Prediction (FBP) System. Two other elements
(Fuel Moisture System and Canadian Forest Fire Occurrence Prediction (FOP)
System) are not developed for the whole country, but there are regional versions
of these systems [17].
The Canadian method of forest fire danger prediction [14] is formed relying on
analysis of a large number of statistical data according to which they formed the
tables of fire danger dependence on different factors. Within the FWI sub-system,
the moisture content of forest fuels is predicted depending on weather conditions;
whereas within FBP, forest fire spots behavior is forecasted for different forest
plant communities.
A logical structure of the system [15, 16] represents an abstract model of the
impact of different factors and conditions on the process of how fire occurs and
spreads.

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The Canadian and American methods are similar to each other in their struc-
ture, approaches and fire danger index formation principles. Therefore, they have
both similar advantages and disadvantages. European Forest Fire Information
System EFFIS (Europe) [6]. The most progressive component of system repeats
the subsystem of the Canadian Forest Fire Danger Rating System. This system
has the same characteristics and uses Earth remote sensing data.
The work purpose is to create a new method for geospatial data analysis
in order to monitor, assess and forecast the forest fire danger caused by storm
activity.

3 Mathematical Methods

Using the basic principles of probability theory, we obtained a formula to assess
the probability for the forest fire to occur for the j-th time interval of the forest
fire season [18]:

𝑃𝑗 = [𝑃 (𝐴)𝑃 (𝐴𝑗 /𝐴) 𝑃 (𝐹 𝐹/𝐴, 𝐴𝑗 ) + 𝑃 (𝐿)𝑃 (𝐿𝑗 /𝐿) 𝑃 (𝐹 𝐹/𝐿, 𝐿𝑗 )] 𝑃𝑗 (𝐷), (1)

where 𝑃𝑗 is the probability of a forest fire to occur for the j-th interval
in the controlled forest area; 𝑃 (𝐴) is the probability of anthropogenic impact;
𝑃 (𝐴𝑗 /𝐴) is the probability of a fire source presence on 𝑗-th day; 𝑃𝑗 (𝐹 𝐹/𝐴, 𝐴𝑗 )
is the probability of a forest fire to occur from anthropogenic impact in the forest
area; 𝑃 (𝐿) is the probability of dry thunderstorms to occur in the forest area;
𝑃 (𝐿𝑗 /𝐿) is the probability of ground lightning discharge; 𝑃𝑗 (𝐹 𝐹/𝐿, 𝐿𝑗 ) is the
probability of a forest fire to occur from lightning in case, if dry thunderstorms
can happen in the forest area; 𝑃𝑗 (𝐷) is the probability of fire to occur due to
weather conditions of forest fire maturation (the probability of the fact that the
forest fuel layer will be dry); index 𝑗 corresponds to a day of the fire danger
season. To determine all multipliers in the formula (1), the author offers to use a
definition of probability through frequency of events and to use statistical data
for a concrete forestry. The formula (1) contains the following members [18]:

𝑁𝐹 𝐷 𝑁𝐴
𝑃 (𝐴𝑗 /𝐴) ≈ , 𝑃 (𝐴) ≈ , (2)
𝑁𝐹 𝑊 𝑁𝐹 𝑆
𝑁𝐹 𝐴
𝑃𝑗 (𝐹 𝐹/𝐴, 𝐴𝑗 ) ≈ , (3)
𝑁𝐹 𝑇
𝑁𝐿𝑁 𝑁𝐿
𝑃 (𝐿𝑗 /𝐿) ≈ , 𝑃 (𝐿) ≈ , (4)
𝑁𝐿𝐷 𝑁𝐹 𝑆
𝑁𝐹 𝐿
𝑃𝑗 (𝐹 𝐹/𝐿, 𝐿𝑗 ) ≈ , (5)
𝑁𝐹 𝑇
where 𝑁𝐴 is the number of days during the fire danger season when the
anthropogenic impact is enough for forest fuel ignition;𝑁𝐹 𝐴 is the number of

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Mathematical and Information Technologies, MIT-2016 — Information technologies

fires from anthropogenic impact; 𝑁𝐹 𝑇 is the total number of fires; 𝑁𝐿 is the
number of days when lightning occurred (during dry thunderstorms); 𝑁𝐹 𝑆 is
the total number of days in the fire danger season; 𝑁𝐹 𝐿 is the number of fires
from lightning (during dry thunderstorms); 𝑁𝐹 𝐷 is the number of fires on a
specific day of the week; 𝑁𝐹 𝑊 is the total number of fires for a week; 𝑁𝐿𝐻 is
a number of ground lightning discharges passed on the concrete hour, starting
from 00.00 oclock; 𝑁𝐿𝐷 is the total number of ground lightning discharges per
day. Obviously, the more cases will be considered for this forestry, the bigger
accuracy to determine the probability by formulas (2)-(5) will be. Therefore, in
forestries, it is necessary to register all fire danger season parameters (𝑁𝐴 , 𝑁𝐹 𝐴 ,
𝑁𝐹 𝑇 , 𝑁𝐿 , 𝑁𝐹 𝑆 , 𝑁𝐹 𝐿 ,𝑁𝐹 𝐷 , 𝑁𝐹 𝑊 , 𝑁𝐿𝐻 , 𝑁𝐿𝐷 ) every year.
Formula (1) contains the multiplier 𝑃𝑗 (𝐷). This is the probability of fire dan-
ger from meteorological conditions. In early work, this probability was calculated
through the time for the forest fuel layer to dry [19]. However, at present, it is
hard to implement the method like this on the whole territory of Russian Feder-
ation, because in order to model the process of drying the forest fuel layer, it is
necessary to have information about the initial moisture content of forest fuel.
The present paper offers to use the compromise variant. We suggest calculating
the probability by meteorological conditions using the Complex Meteorological
Index, which was approved in the state standard. The range of this index starts
from zero and has no upper border. However, it is possible to set its upper bor-
der as a maximum possible value during the fire danger season. To estimate the
probability of forest fire danger, we normalize the complex meteorological index
on figure of one [18]:
𝑁 𝐼𝐷
𝑃𝑗 (𝐷) = , (6)
𝑁 𝐼𝑚𝑎𝑥
where 𝑁 𝐼𝐷 is a value from the complex meteorological index for the day for
which the forecast is realised; 𝑁 𝐼𝑚𝑎𝑥 is the maximum value of the complex me-
teorological index. Then, the range of variation of forest fire danger probability
by meteorological conditions will be within 0 to 1.
The complex meteorological index is calculated by the formula [7]:
∑︁
𝑁𝐼 = 𝑡(𝑡 − 𝑟), (7)
𝑛
where 𝑡 is the air temperature; 𝑟 is the dew point temperature; 𝑛 is the
number of days after the last rain.
The dew point characterises the amount of moisture in the air. The higher
the dew point, the greater the humidity is at a given temperature. The dew
point temperature is determined as the temperature to which air must be cooled
(at the constant pressure and constant water vapour content), in order to reach
saturation and in order for its condensation process to start, that is, the dew to
appear. The saturation state can exist only as long as the air contains the max-
imum possible amount of water vapour at the given temperature and pressure.
The work [20] suggests a simple mathematical model of tree ignition by the
cloud-to-ground lightning discharge.

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Mathematical and Information Technologies, MIT-2016 — Information technologies

Electric current flow is various in the trunk of deciduous and coniferous trees
[21]. This is due to the fact that in broad-leaved trees, moisture is transported is
in a massive central part. More damp central part is an electric current conduc-
tor. The analysis of the known information on wood properties of broad-leaved
species shows, that it is necessary to consider moisture presence in the trunk
wood structure. Even under the conditions of high-speed processes, moisture
presence can essentially change the wood ignition conditions. Therefore, when
setting the task for broad-leaved trees, it is expedient to consider the influence
of moisture content on thermophysical characteristics of wood.
We consider the following physical model. A cloud-to-ground lightning dis-
charge strikes in a tree trunk at the fixed moment of time. The electric current
of the cloud-to-ground lightning discharge flows along the trunk. It is supposed,
that the heat emits in the core according to Joule-Lenz law. It is supposed that
in various trunk sections, the electric current has the same parameters. It is con-
sidered, that one can describe the moisture evaporation by Knudsen-Lengmuir
equation [22]. As a result of electric current flow, the wood is warmed up due to
the Joule heat emission and the wood ignites when achieving the critical ther-
mal fluxes to ignition surface and critical temperature. It is supposed, that the
formed vapor space is filled with water vapor. Changes of volume fractions of
phases are reflected on thermophysical properties of internal wood part of the
broad-leaved tree. The tree trunk is modeled by the cylinder. We consider the
representative section of a trunk. Fig. 1 shows the decision area scheme.

z
1

Rs
0 R1 r

Fig. 1. The decision area scheme: 1 core, 2 - bark.

The system of non-stationary differential equations mathematically describes
the process how a cloud-to-ground lightning discharge warms up a tree trunk
before ignition [20]:
(︂ )︂
𝜕𝑇1 𝜆𝑒𝑓 𝜕 𝜕𝑇1
𝜌𝑒𝑓 𝑐𝑒𝑓 = 𝑟 + 𝐽𝑈 − 𝑄𝑊 𝜙2 , (8)
𝜕𝑡 𝑟 𝜕𝑟 𝜕𝑟

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Mathematical and Information Technologies, MIT-2016 — Information technologies

(︂ )︂
𝜕𝑇2 𝜆2 𝜕 𝜕𝑇2
𝜌2 𝑐2 = 𝑟 , (9)
𝜕𝑡 𝑟 𝜕𝑟 𝜕𝑟
𝜕𝜙1
𝜌3 = 0, (10)
𝜕𝑡
𝜕𝜙2
𝜌4 = −𝑊, (11)
𝜕𝑡
5
∑︁
𝜙𝑖 = 1, (12)
𝑖=3

𝐴(𝑃 5 − 𝑃 )
𝑊 = √︁ , (13)
2𝜋𝑅𝑇
𝑀

𝜌𝑒𝑓 = 𝜌3 𝜙3 + 𝜌4 𝜙4 + 𝜌5 𝜙5 , 𝜆𝑒𝑓 = 𝜆3 𝜙3 + 𝜆4 𝜙4 + 𝜆5 𝜙5 . (14)
Boundary conditions for the equations (1) - (2):
𝜕𝑇1
𝑟 = 0, 𝜆𝑒𝑓 = 0; (15)
𝜕𝑟
𝜕𝑇1 𝜕𝑇2
𝑟 = 𝑅1 , 𝜆𝑒𝑓 = 𝜆2 , 𝑇1 = 𝑇2 ; (16)
𝜕𝑟 𝜕𝑟
𝜕𝑇2
𝑟 = 𝑅, 𝜆2 = 𝛼(𝑇𝑒 − 𝑇𝑅𝑠 ). (17)
𝜕𝑟
Initial conditions for the equations (1) – (5):

𝑡 = 0, 𝑇𝑖 (𝑟) = 𝑇𝑖0 ), 𝜙𝑖 (0) = 𝜙𝑖0 . (18)
Where 𝑇𝑖 is temperature of internal part of tree trunk (𝑖 = 1) and bark
(𝑖 = 2); 𝜙𝑖 - volume fraction: organic substance (𝑖 = 3), water (𝑖 = 4) and water
vapor (𝑖 = 5); 𝜌𝑖 , 𝑐𝑖 , 𝜆𝑖 is density, thermal capacity and heat conductivity of
bark (𝑖 = 2), organic substance (𝑖 = 3), water (𝑖 = 4) and water vapor (𝑖 = 5);
𝜌𝑒𝑓 , 𝑐𝑒𝑓 , 𝜆𝑒𝑓 - effective density, thermal capacity and heat conductivity of wood
for internal part of trunk; 𝜆 - heat transfer factor; 𝐽 current strength; 𝑈 -
voltage; 𝑄 - thermal effect of moisture evaporation; 𝑟 - coordinate; 𝑡 - time. 𝑊 -
mass speed of water evaporation, 𝐴 - accommodation coefficient, 𝑃 𝑠 - pressure
of saturated water vapor, 𝑃 - partial pressure of water vapor in air, 𝑅 - universal
gas constant, 𝑀 - molecular weight of water. Indexes 𝑅𝑠, 𝑒 and 0 correspond to
the parameters on the external border of tree trunk, the environment and to the
parameters at the initial moment of time.
Formulated system of equations (8) – (14) with boundary and initial condi-
tions (15) – (18) is solved by the finite difference method [23]. The double-sweep
method in combination with the fixed point iteration method [23] was used to
decide the difference analogues of one-dimensional equations.

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The following ignition scenario was considered. The negative cloud-to-ground
lightning discharge, with duration of 500𝑚𝑠, with peak current of stroke in 23.5𝑘
and voltage 100𝑘𝑉 , influences on a wide-leaved tree, for instance, birch. Fig. 2
shows the temperature distribution on the tree trunk radius in various moments
of time before and at the moment of igniting by electric current (initial temper-
ature 300𝐾).

1300

1200
a

1100 b

c
1000 d

900
T, K

800

700

600

500

400

300

0,230 0,235 0,240 0,245 0,250

r, m

Fig. 2. Temperature distribution on the tree trunk radius at the various moments of
time (discharge action duration is 500𝑚𝑠): a - 𝑡 = 0.01𝑠; b - 0.1𝑠; c - 0.3𝑠; d - 0.5𝑠 [20].

Table 1 represents the lightning discharge parameters and ignition conditions
depending on voltage of ground-to-cloud lightning discharge obtained by solving
the problems (8) – (14). The analysis of dependences presented on Fig. 2 shows,
that tree trunk is warmed up to ignition temperature (more than 1000𝐾) by
the action of the considered cloud-to-ground lightning discharge. The analysis
of results shows that for a typical cloud-to-ground lightning discharge, ignition
conditions of wide-leaved tree are reached on critical temperature (801𝐾) and
value of thermal flux (268𝑘𝑊/𝑚2 ).
We established the ignition limits for tree trunk during the action of the
electric discharge at various voltages (Table 1) and current. When the current is
less than 15𝑘𝐴 and voltage is 1 − 50𝑘𝑉 , ignitions fail to occur during the action
of cloud-to-ground lightning discharge.

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Table 1. Ignition condition of tree depending on voltage of the discharge at current
𝐽 = 23.5𝑘𝐴 [20]

Voltage, 𝑈, 𝑘𝑉 Ignition condi- Surface tempera- Heat flux from
tions ture, core to surface, k
𝑘𝑊/𝑚2
1–45 No < 801 < 201
50 No < 801 252
55 Yes 801 268
60 Yes 801 268
80 Yes 801 268
100 Yes 801 268
110 Yes 801 268

3.1 GIS System

Program realization of mathematical model for quantitative assessment of prob-
ability of forest fire danger caused by storm activity is enabled in GIS.
Algorithms of geographical information system for quantitative assessment
of forest fire danger are implemented in the Python language embedded into
ArcGIS [24]. The quantitative assessment is carried out relying on the remote
sensing data, land mensuration of forests and statistical information. The criteria
to assess the forest fire danger are defined relying on the probability theory, and
its values are within the range from 0 to 1. Calculations are made with accuracy
up to 0.0001.
Below are the tables in the MS Excel format with forest mensuration de-
scriptions on stratums (Table 2). Russian database on stratums description is
used.
The program tool “FFstormactivity.tbx” solves the problem to forecast the
fire danger of forest quadrant relying on the information about stratum com-
position and statistical information on fires caused by storm activity and the
display of the obtained information on the electronic map. Python is the source
language of the “FFstormactivity” program [24].
The program tool “FFstormactivity” contains 7 forms. It provides two vari-
ants to solve the task: complex and stage-by-stage with the control of result.
Main stages:

1. Data import from the table Excel to the autonomous geodata base table.
2. Determination of fire danger for forest stratum.
3. Assessment of fire danger probability for forest quadrant according to forest
mensuration descriptions.
4. Import of statistical data to geodata base.
5. Assessment of fire danger probability caused by storm activity.
6. Connection of attributive and autonomous tables.
7. Formation of the map according to a legend.

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Table 2. Tables of forest mensuration data in the MS Excel format.

forestry quarter site area composition age
Kaltayskiy 1 1 43.7 Grass
Kaltayskiy 1 2 2 Wetland
Kaltayskiy 1 3 7.6 7B2L1P 𝐵 − 75,𝐿 − 120,
𝑃 − 120
Kaltayskiy 1 4 14.8 7W3B 𝑊 − 30, 𝐵 − 35
Kaltayskiy 1 5 19 7W3B 𝑊 − 30, 𝐵 − 35
Kaltayskiy 1 6 18.3 8B2L 𝐵 − 65, 𝐿 − 120
Kaltayskiy 1 7 5.5 7B2L1P 𝐵 − 75, 𝐿 − 120,
𝑃 − 120
Kaltayskiy 1 8 5.6 5P21L2B 𝑃 − 140, 𝐶 − 160,
𝐿 − 140, 𝐵 − 75
Kaltayskiy 1 9 5.3 5C2F1P2B 𝐶 − 180, 𝐹 − 140,
𝑃 − 140, 𝐵 − 85
Kaltayskiy 1 10 1.2 Lake

First step is data import from the table Excel to the autonomous geodata
base table.
Next step is determination of fire danger for stratum according to forest men-
suration descriptions and assessment of fire danger probability of forest quadrant
according to forest mensuration descriptions.
Third step is import of statistical data on storm activity to geodata base.
Algorithm of assessment of probability of the fire danger caused by storm
activity presented on Fig. 3.
Last stages are connection of attributive and autonomous tables and forma-
tion of the map according to the legend.
The program tool FFstormactivity uses the following methods:

1. AddField is to add a field. The program adds a field.
2. CalculateField is to calculate the field value. To determine the fire danger of
the stratum, to assess the probability of forest fire danger on the quadrant,
of the level.
3. Statistic analysis is the total statistics. To calculate the total quantity of
stratums in each quadrant and quantity of the fire-dangerous ones.
4. JoinField is to connect the fields. A connection of two tables takes place on
the basis of a key field
5. ApplySymbologyFromLayer management is to add the layer symbols. To form
the layer of quadrants according to the fire danger level.

The start-up of the program tool comes from ArcToolbox. It is necessary to
specify the initial data in the dialog window that appears after start-up. Russian
interface is used in current version of GIS-system.
Structures of tables with initial data on forest fires and forest mensuration
descriptions of the territory are given below (Table 3 and Table 4).

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Mathematical and Information Technologies, MIT-2016 — Information technologies

Fig. 3. Assessment of probability of the fire danger caused by storm activity.

The tool implementation results in creating the table with an assessment
of probability of fire danger of forest quadrant caused by storm activity with
regard to the forest vegetation conditions and the thematic map displaying the
fire danger levels of forest quadrants ( Fig. 4).
The forest fire danger levels in Fig. 4 correspond to the following gradation:
1 - 0,001852 - 0,030000 2 - 0,030001 - 0,060000 3 - 0,060001 - 0,090000 Minimum
- 0,001852; maximum - 0,08333.

4 Discussion
The analysis of foreign forest fire danger forecast systems shows that in the ter-
ritory of their states they show high operational qualities. However, it is difficult
to apply them in the territory of other states, as it is necessary to carry out
all range of works on the analysis and adjustment of empirical formulas for new
forested territories.
All foreign systems finally offer an abstract index of forest fire danger. The
present paper offers the new probabilistic approach to assess the most probable

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Mathematical and Information Technologies, MIT-2016 — Information technologies

Table 3. . Structure of the table with statistical data on the fires in the MS Excel
format.

Name forest Name of fores district
NF A total number of the fires
during a fire-dangerous
season
N FA Number of the fires from
storm activity during a
fire-dangerous season
ND Total number of days of a
fire-dangerous season
NA number of days during a
fire-dangerous season when
there is a storm activity
sufficient for ignition of for-
est fuel
N1 Monday
N2 Tuesday
N3 Wednesday
N4 Thursday
N5 Friday
N6 Saturday
N7 Sunday
NW Total number of fires per a
week

Table 4. Structure of the table with initial data on stratums in the MS Excel format.

forestry quarter site area compisition age

scenarios of forest fire danger. The definite scenario can be calculated using a de-
terministic mathematical model of how the cloud-to-ground lightning discharge
ignites a tree.
We developed GIS-system for forecasting the forest fire danger caused by
storm activity. The system reserves the layers for the subsequent implementation
of a deterministic component based on the mathematical model of tree ignition
by cloud-to ground lightning discharge.

Conclusion. As a result of research, we offered the new physically proved ap-
proach to forecast the forest fire danger caused by storm activity. The analysis
of the methods based on statistical data shows that it is impossible to ade-
quately assess the probability of forest fires caused by storm activity. We offered
to use the deterministic models of tree ignition by a cloud-to-ground lightning

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Mathematical and Information Technologies, MIT-2016 — Information technologies

Fig. 4. Map of forest fire danger caused by storm activity in the territory of the
Timiryazevskiy local forestry of the Timiryazevskiy forestry of the Tomsk region.

discharge and probabilistic criterion of forest fire danger assessment. The anal-
ysis of statistical approach is carried out in the territory of the Timiryazevskiy
local forestry of the Timiryazevskiy forestry of the Tomsk region. Technologies
of geographic information systems are used to visualize the spatial data. The
program implementation of algorithms is enabled in the ArcGIS software.

Acknowledgements. This research implemented with financial support by
Russian Foundation for Basic Research. Grant 16-41-700831.

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