=Paper=
{{Paper
|id=Vol-3006/20_regular_paper
|storemode=property
|title=Nonlinear approximation of wildfire front temperature on MODIS data for sub-pixel analysis of burning
|pdfUrl=https://ceur-ws.org/Vol-3006/20_regular_paper.pdf
|volume=Vol-3006
|authors=Kirill Yu. Litvintsev,Evgenii I. Ponomarev,Evgenii G. Shvetsov
}}
==Nonlinear approximation of wildfire front temperature on MODIS data for sub-pixel analysis of burning==
https://ceur-ws.org/Vol-3006/20_regular_paper.pdf
Nonlinear approximation of wildfire front
temperature on MODIS data for sub-pixel analysis of
burning
Kirill Yu. Litvintsev1 , Evgenii I. Ponomarev2,3 and Evgenii G. Shvetsov2
1
S.S. Kutateladze Institute of Thermophysics SB RAS, Novosibirsk, Russia
2
V.N. Sukachev Institute of Forest, Federal Research Center βKrasnoyarsk Science Center SB RASβ, Krasnoyarsk, Russia
3
Siberian Federal University, Krasnoyarsk, Russia
Abstract
An improved approach to evaluate thermal anomalies characteristics using the pixel-based analysis
of the MODIS imagery was proposed. The approach allows us to improve the accuracy in estimating
characteristics of active combustion zones comparing to the standard Dozier method. We used the
imagery of active wildfires in Siberian forests from the MODIS radiometer acquired in the spectral ranges
of 3.930β3.990 and 10.780β11.280 πm (bands 21 and 31, respectively). Nonlinear exponential function was
used to describe the approximation of the temperature of combustion zones. Available data of field and
numerical experiments were used for validating of the approximation accuracy. Nonlinear approximation
of wildfire front temperature allows to determine the portion of the active pixel of the MODIS image
with the given temperature excess comparing to the temperature of background cover. This improves
the accuracy in extracting of active burning zones as well as in classifying the heat release rate at the
sub-pixel level of analysis.
Keywords
Remote data, active combustion zone, wildfire, radiation, sub-pixel analysis.
1. Introduction
Detection of vegetation fires and instrumental estimation of combustion characteristics is one of
most important directions of the thematic analysis of remote sensing data [1, 2]. The resolution
of specialized satellite systems used in fire monitoring as a rule does not exceed 250 m, and the
best known Russian platforms of forest fire monitoring (βISDMβ of the Federal Forestry Agency
and βKaskadβ of the Russian Ministry of Emergency Situations) handle satellite information
with a spatial resolution of 1000 m, which, at present, determines a limited set of available
attributive parameters of fires β coordinates, area, and time. Early detection of wildfires is
significantly limited because their characteristics can be detected only when carrying out the
subpixel analysis based on reliable models of the integral signal formation in the image pixel
including the small-size source of thermal anomaly. Theoretically [3], satellite methods allow us
to discover a hot spot with an area of 100 m2 ; in practice, according to estimates, the probability
of detection a hot spot with an area of 5000 to 6000 m2 and temperature of 700 K is 60β70% [4].
SDM-2021: All-Russian conference, August 24β27, 2021, Novosibirsk, Russia
" sttupick@yandex.ru (K. Yu. Litvintsev); evg@ksc.krasn.ru (E. I. Ponomarev)
Β© 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073 CEUR Workshop Proceedings (CEUR-WS.org)
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Kirill Yu. Litvintsev et al. CEUR Workshop Proceedings 161β171
Development of new approaches for the effective estimation of hot spot parameters at different
stages of fire growth remains a topical problem [5, 6, 7]. At present, only a few works are
available regarding recording and processing data on the energy characteristics of thermally
active zones in case of fires in boreal forests [8, 9, 10], although the method was tested many
times on the example of experimental fires with known characteristics [5, 11]. Therefore,
development of methods for instrumental quantitative estimates of fire characteristics is at
present not a completely solved problem in spite of the fact that works in this direction have
been carried out since the second half of the 20th century [12, 13, 14].
In this work, we consider the problem of approximating the temperature distribution of the
active combustion front to improve the classification of thermally active zones at the subpixel
level and estimating the heat release rate at different fire phases. Based on the numerical
calculations, the effectiveness of the nonlinear distribution function in interpreting MODIS
(Moderate Resolution Imaging Spectroradiometer) imagery data for the determination of fire
characteristics is analyzed. The main goal of the work is to improve the method of the subpixel
analysis of MODIS data. Our objectives were to: (1) approximate the temperature profile of
the active combustion zone perpendicularly to the fire front propagation direction and (2) to
compare the effectiveness of the subpixel detection of thermal anomalies based on the proposed
and standard [13] approaches.
2. Description of the nonlinear approximation and initial data
This work involves the field data collected on vegetation fires in Siberia according to the results
of processing the MODIS imagery during the period from 2003 to 2018 [15].
In addition, standard MODIS products of the L2G and L3 processing levels were analyzed. Pixel
data on radiometric temperature in the ranges π = 3.93 β 3.99 (radiometer band 21) and 10.78β
11.28 πm (band 31) were calculated from the MOD11A1 product [16]. The radiative power of
active combustion zones were determined from MOD14/MYD14 Collection 6 products [17]. From
the MODIS thermal anomaly products we obtained fire radiative power (FRP) characterizing
the thermal emission power and combustion rate [11, 18]. Using the bispectral method [13] we
performed subpixel analysis for the MODIS active fire pixels. The characteristics of the fire
front were additionally refined based on Sentinel-2 imagery.
Based on the obtained and processed satellite data, the effectiveness of the determination
of the energetic and geometric characteristics of fires was analyzed. At the first stage, pixels
corresponding to the wildfires were identified; then, the active subpixel portion allowing us to
estimate the areas and rates of the active combustion zone was determined. For this purpose,
the bispectral method [13] was used. It estimates the characteristics of active fire zone in a
MODIS pixel based on the values of the averaged temperature of the target and background.
The solution is based on analyzing the rate of radiation of the active combustion zone. The rate
is determined for the wavelength in the IR range π1 and π2 :
πΏπ1 = πΌ Β· πΏ(π1 , ππ ) + (1 β πΌ) Β· πΏ0π1 ,
{οΈ
(1)
πΏπ2 = πΌ Β· πΏ(π2 , ππ ) + (1 β πΌ) Β· πΏ0π2 ,
π
πΏ(π, π ) = (οΈ π12 )οΈ ,
π5 Β· π πΒ·π β 1
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where πΏ(π, π ) is the Planck formula for the radiance, W/(m3 Γsr); πΌ is the portion of the active
zone in the pixel; πΏπ1 and πΏπ2 are the radiation rates recorded in the ranges π1 and π2 ; πΏ0π1 and
πΏ0π2 are the background radiation rates in the given ranges, respectively; ππ is the averaged
temperature of the active combustion zone; π1 = 1.19Γ10β16 WΓm2 , π2 = 14.388Γ10β2 mΓK.
The main assumption of the bispectral method [13] is the uniform distribution of the surface
temperature in the active combustion zone (Figure 1). This can lead to a significant error in
calculations of the fire area because the temperature distribution profile is not uniform. In this
work, the temperature profile was approximated by nonlinear exponential function (Figure 1):
[οΈ(οΈ )οΈ π1 ]οΈβ1
π1 π2 β ππ1 (π¦)π2
(οΈ π¦ )οΈπ1
π (π¦, πmax ) = (πmax β π0 ) Β· Β·π 2 Β· Β· πβ πΏπ2 + π0 , πΏ > 0, (2)
π2 πΏ
where the parameters π1 and π2 are responsible for the steepness of the front edge of the
active fire zone and uniformity of the temperature profile, respectively; πmax is the maximum
temperature, π0 is the background temperature; πΏ > 0 is the parameter
βοΈ characterizing the
linear width of the active zone front, m; and π¦(π = πmax ) = β 2 π2 Β· πΏ is the coordinate of
π π1
the temperature maximum. When using this approximation, it is assumed that the width of
the fire front is significantly less than its length. In this case, with allowance for (2), Eq. (1) is
modified as follows:
πΏπ1 = πΌ Β· πΌΒ―(π1 , πmax ) + (1 β πΌ) Β· πΌπ1
0 ,
{οΈ
(3)
πΏπ2 = πΌ Β· πΌΒ―(π2 , πmax ) + (1 β πΌ) Β· πΏ0π2 ,
β«οΈπ¦2
1 1.19 Β· 10β16
πΏ(π, πmax ) = Β· (οΈ )οΈ ππ¦, (4)
π¦2 β π¦1 5
1.44Β·10β2
π¦1 π Β· π β1
πΒ·π (π¦,π max )
Figure 1: General form of the surface temperature approximation in the region of an active subpixel
according to [13] and using a nonlinear exponential function perpendicularly to the fire front propagation.
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where π¦1 = 0 and π¦2 = 3πΏ. In the case where π¦1 and π¦2 are linear functions of πΏ, the value πΌΒ―
does not depend on πΏ.
Values of the parameters π1 = 1.3 and π2 = 2 were obtained based on the generalization
of experimental data for fires in Siberia [19]. Following the results of the generalization,
model temperature curves were obtained (Figure 2). In general, the proposed approximation of
temperature allows us to sufficiently closely reproduce the temperature profile of the fire front.
This approximation ignores low-rate combustion/smoldering regions, which are observed as a
rule behind the fire front (Figure 2).
In the solution of the system of equations (3), the magnitude of the active portion of pixel πΌ,
in contrast to the standard method [13], in fact does not determine the combustion region but
characterizes the subpixel region with a temperature exceeding the background temperature.
To determine the portion of the pixel with a given excess of the temperature Ξππ over the
background, it is necessary to find roots of Eq. (5) π¦πΌ1 and π¦πΌ2 in the interval (π¦1 ; π¦2 ):
[οΈ(οΈ )οΈ π1 ]οΈβ1
π1 π2 β ππ1 (π¦)π2
(οΈ π¦ )οΈπ1
(πmax β π0 ) Β· Β·π 2 Β· Β· πβ πΏπ2 β Ξππ = 0. (5)
π2 πΏ
After the calculation of π¦πΌ1 and π¦πΌ2 the portion of the region πΌπ with the given Ξππ is deter-
mined as follows:
|π¦πΌ2 β π¦πΌ1 |
πΌπ = πΌ Β· . (6)
3πΏ
The ratio of active pixel portions calculated by Dozierβs method (πΌπ· ) and modified bispectral
method (πΌπ ) with the temperature excess over the background Ξππ is determined as:
πΌπ
π΄Ξπ = . (7)
πΌπ·
Figure 2: Surface temperature distribution: field measurement data [19] and their nonlinear approxi-
mations. The extreme values of the temperature measurement data correspond to the fire front and
residual spots of combustion and smoldering behind the fire front.
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To verify the proposed nonlinear approximation, available data of field measurements and
numerical simulations of the temperature distribution on the surface during a surface fire were
considered.
To evaluate the effectiveness of the proposed approach, the comparative analysis of the
subpixel characteristics (temperature and area of the active combustion zone) and results of the
standard bispectral method [13] was carried out. It involved a sample of pixels from MODIS
images containing more than 23000 hot spots. The considered image pixels corresponded to
fires detected in Krasnoyarsk Angara Region (mainly, fires in pine forest stands), Evenkiya
region (fires in larch forests), and the left bank of the Yenisei River.
The power of fire radiation from a unit area of the active combustion zone was estimated
using the standard bispectral method [13] and the method with the nonlinear approximation
of temperature with the use of different threshold excesses of the temperature to extract the
active combustion zone. This sample contained 9500 MODIS fire pixels. For each pixel, values of
the fireβs radiative power (FRP) were determined and sub- pixel areas of the high-temperature
zone were calculated using the considered methods. Calculation of the areas by the proposed
modified method involved the following values of threshold temperatures for the determination
of the active combustion zone: 50, 100, 160, and 200 β C. The fire radiative power from a unit
area was calculated as the ratio of the total heat release power of a fire pixel to the area of the
high-temperature zone.
3. Results and discussion
The spatial resolution of satellite systems does not allow us to directly obtain the fire data of
this kind with the required accuracy. So, below, the fire frontβs temperature profiles (Figure 2)
approximated based on field measurements [19] are used as a calibration of satellite acquisition
materials.
To verify the nonlinear approximations were compared with field measurement data obtained
by low speed wind tunnel at Riverside Fire Laboratory [20] (Figure 3, a) and with numerical
simulation results of a fire spread through a grassland [21], (Figure 3, b). Coefficients π1 and π2 in
a b
Figure 3: Surface temperature distribution: a β field measurement data [20] and its nonlinear approxi-
mations; b β numerical simulation data [21] and its nonlinear approximations.
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Table 1
Characteristics of variation in temperature and area of the active zone for the used test sample of pixels
corresponding to the active fire phase.
MODIS π, K Temperature variation over the sample (π , K)
band average π median min max percentile 10 percentile 90
21 326.9 20.4 321.3 305.0 502.3 309.4 351.0
31 294.6 6.3 295.2 271.2 400.1 286.7 301.6
21* 298.7 6.9 300.4 276.3 320.0 288.8 306.7
31* 291.9 5.9 292.7 268.3 306.7 283.9 298.9
π, km2 Variation in the active zone area over the sample (π, km2 )
1.9 1.4 1.3 1.0 9.7 1.0 3.5
*
Measurements of background values.
the equation (2) not were changed. The data from [20, 21] in Figure 3 is the surface temperature
profile averaged along the fire front. Despite the different scales of the considered fires and
different fuel beds (pine needles [20] and grass [21]), the nonlinear approximation describes
their temperature profiles well enough.
The statistical characteristics of active fire zone parameters (data of the MODIS bands 21
and 31) recorded for the test sample are presented in Table 1. Since the subpixel analysis used
in this work is applicable only for surface fires, the table presents characteristics of fire pixels
with the exception of the maximum temperatures (above the 90th percentile). This excluded the
portion of pixels that corresponded with a high degree of probability to the crown fire phase
that we do not deal with [10].
The obtained data did not take into account the influence of the scanning angle on the
estimate of the area of the ground projection of the MODIS pixel because the error is not
accumulated when the calculation results obtained for the subpixel analysis based on the
considered approaches are compared. At the same time, it is known that the area of the pixel
projection increases with an increase in the scanning angle (deviation from nadir). This, in
the general case, leads to a decrease in the fraction of the area occupied by the fire bed within
the limits of the pixel and, therefore, to a decrease in the contrast between the fire pixel
and background in the thermal IR range. Due to the comparison of the two approaches, this
uncertainty in fact had no effect on the results of the comparative analysis. In spite of the fact
that the sample was not limited in the maximum scanning angle, the deviation from nadir for
the main part (68%) of MODIS pixels used in the analysis was within 300 and their area did not
exceed 1.7 km2 . The average area amounted to about 1.9 km2 .
The quantitative analysis of the processed fire pixels for which the portion of the active
subpixel was determined using the method [13] and modified bispectral method with a threshold
excess of the temperature over the background Ξππ demonstrates that the main part of the
coincidence falls on values Ξππ in the interval from 60 to 160 β C. Up to 15% of the pixels were
detected outside the above-mentioned range (Figure 4). We can say that the concept of the active
pixel portion has no clear definition when the standard method [13] is used because there is in
fact no given referencing to the energy characteristics of the fire. The high-temperature region
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Figure 4: Distribution of pixels over intervals Ξππ (β C) for which portions of active subpixels calculated
by the standard (Dozier, 1981) and modified methods coincide.
which is taken into account in this method depends on the calculated average temperature
determined to a considerable extent by the fireβs intensity.
Figure 5 shows the dependence of the ratio π΄Ξπ (see (7)) on the averaged temperature for
different Ξππ in the modified method. In particular, for Ξππ = 60 β C, the coincidence of the
methods is observed in the interval of averaged temperatures of 420 to 450 β C; for Ξππ = 140 β C,
in the interval of 600 to 630 β C. For example, if we assume that an active subpixel is characterized
by temperature exceeding the background values by 60 β C, the difference between the results of
the two methods reaches 40% (Figure 5). In general, the overestimation of the active pixel portion
Figure 5: Relationship of pixel portions when using the nonlinear and standard approximations of
temperature in the active combustion region for the bispectral method. Ξππ is equal to 60 and 140 β C.
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Figure 6: Ratio of the threshold temperature to the averaged temperature calculated by the method
of [13] as a function of the fire intensity, the background temperature π0 equals 300 K (the linear
structure of the distribution is related to the interval-by-interval approximation of temperature).
in the standard approach is inversely proportional to the variation of the parameter Ξππ .
If we consider the dependence of the ratio of Ξππ (when πΌπ (Ξππ ) β πΌπ· ) to the averaged
temperature ππ· , then this quantity varies with a relatively small range from 0.4 to 0.5. Therefore,
based on the given πmax for the modified method, we can calculate Ξππ for which the condition
πΌπ (Ξππ ) β πΌπ· is satisfied; i.e., the active subpixel portion is close to that calculated by the
method of [13] (Figure 6). The nonlinear approximation of temperature, as noted above, is more
effective because it is physically closer to the real temperature distribution on the surface of the
active zone than the approximation used in the standard approach.
Another important problem related to the nonuniformity of the temperature distribution is
the determination of Ξππ for the active portion of the fire pixel. We can use two approaches:
specifying the Ξππ and calculating Ξππ from the condition of falling within the temperature
range above π0 + Ξππ , providing more than 95% of the radiation energy of the considered range
of π. For example, when using the second approach with πmax of about 720 β C, Ξππ = 235 β C;
at πmax = 450 β C, Ξππ is only 64 β C.
The results of the performed analysis demonstrate that the representation of the fire region
as a region with a uniform temperature can lead to a significant error when estimating the
active zone area at the subpixel level and intensity of the acting fire front. In particular,
it is seen from the dependences presented in Figure 1 that the area of the active zone for
the uniform approximation corresponds to an excess of about 60 β C over the background
temperature compared to the nonlinear approximation; the averaged temperature here is lower
than the maximum temperature approximately by 170 β C. These deviations vary depending
on the recorded values of the radiation intensity. Therefore, the uniform distribution in each
case determines the active zone area with an unknown temperature which cuts off the low-
temperature region. Using a nonuniform approximation of the temperature distribution on the
surface for the active combustion zone, in contrast to a uniform approximation, allows us to
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separate regions with different levels of the given temperatures, e.g., the region of high-intensity
combustion.
The major part of the considered fire pixels was characterized by the fireβs radiative power
values of up to 10 kW/m2 (about 80% for larch forests of Evenkiya and about 65% for pine forests
of the Angara Region). It has been found that, for the fire pixel sample used in the analysis, the
subpixel area obtained by the standard bispectral method corresponds to the results obtained
according to the method considered in this paper at the threshold temperatures of 120 to 140 β C.
At lower threshold temperatures (50 and 100 β C), the estimates of the subpixel areas were larger
than according to the standard method and, as a consequence, the portion of pixels with low
thermal radiation intensity (up to 5 kW/m2 ) increased. At the same time, the higher values of
the temperature threshold (160 and 200 β C) yielded lower estimates of the sub-pixel area and
higher thermal radiation intensities. In particular, at the threshold value of 200 β C, most fire
pixels pass to the category of 5 to 10 kW/m2 .
4. Conclusions
The effectiveness of the subpixel analysis of the MODIS data based on the bispectral method in
the problem of detection and description of thermal anomalies can be increased with the use of
the nonlinear approximation of the temperature of the active fire zone. This approximation
is shown that it describes quite well the surface temperature profile of the surface fire front
propagation for the considered set of field and numerical data. By the example of the proposed
nonlinear exponential approximation, it is shown that, in contrast to the standard method,
only such an approach allows us to specify the determination of the active pixel portion of the
MODIS image either via the excess of temperature in it over the background temperature or via
the portion of the radiation energy. The discrepancy in the determination of the active pixel
portion when using the considered approaches reaches tens of percent, which has a significant
effect on the final classification of the heat release rate at the subpixel level according to the
phases of the fireβs evolution (e.g., phases recorded remotely in an expeditious manner).
At present, the main problem in using the nonlinear approximation of temperature is the
accumulation of the empirical and calculated data on the temperature distribution on the surface
in the active combustion zone for different types of natural fires with the aim of refining the
proposed approximation function or creating a family of such functions.
Acknowledgments
This research was partly funded by the Russian Foundation for Basic Research (RFBR) and
Government of the Krasnoyarsk krai, and Krasnoyarsk krai Foundation for Research and
Development Support, No. 20-44-242002.
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