Methodology for determining classes of forest fire risk using the modified Monte Alegre Formula

Abstract

The objective of this study was to calculate the Modified Monte Alegre Formula (FMA⁺) and adjust the wildfire risk classes of areas of forests planted in the northern-central coast of the state of Espírito Santo state and the southern coast of Bahia state. The methodology used included six stages: risk calculation; spreadsheet development according to the occurrence, or not, of forest fires; spreadsheet development according to the wildfire season in the study region; risk class definition; result analysis of the determined classes; best fit selection. It was observed that the class definition methodology for the FMA⁺ system obtained excellent results. It increased by 19.3, 21.53, and 31.3% for the percentage of success for subzones 1, 2, and 3, respectively, which implies this an important study for the successful implementation of FMA⁺ in other areas.

_______________________________________________________________________________________

O objetivo deste estudo foi calcular a Fórmula Modificada de Monte Alegre (FMA⁺) e ajustar as classes de risco de incêndio em áreas de florestas plantadas na costa norte-central do estado do Espírito Santo e na costa sul do estado da Bahia. A metodologia utilizada incluiu seis etapas: cálculo de risco; desenvolvimento de planilhas de acordo com a ocorrência, ou não, de incêndios florestais; desenvolvimento de planilhas de acordo com a estação de incêndios florestais na região estudada; definição de classe de risco; análise de resultados das classes determinadas; seleção de melhor ajuste. Observou-se que a metodologia de definição de classe para o sistema FMA⁺ obteve excelentes resultados. Aumentou em 19,3; 21,53 e 31,3% para o percentual de sucesso nas subzonas 1, 2 e 3, respectivamente, o que traduz em resultados este importante estudo para a implementação bem-sucedida da FMA⁺ em outras áreas.

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Ci. Fl., Santa Maria, v. 30, n. 4, p. 1085-1102, out./dez. 2020
ISSN 1980-5098
DOI: https://doi.org/10.5902/1980509839899
Submissão: 06/09/2019 Aprovação: 20/07/2020 Publicação: 1º/12/2020
Artigos
Methodology for determining classes of forest re risk using the modied
Monte Alegre Formula
Metodologia para determinação das classes de risco de incêndio orestal usando
a Fórmula de Monte Alegre modicada
Fernando Coelho EugenioI, Alexandre Rosa SantosII,
Beatriz Duguy PedraIII, José Eduardo Macedo PezzopaneIV,
Cássio Carlette ThiengoV, Nathália Suemi SaitoVI
Abstract
The objective of this study was to calculate the Modied Monte Alegre Formula (FMA⁺) and adjust the
wildre risk classes of areas of forests planted in the northern-central coast of the state of Espírito Santo
state and the southern coast of Bahia state. The methodology used included six stages: risk calculation;
spreadsheet development according to the occurrence, or not, of forest res; spreadsheet development
according to the wildre season in the study region; risk class denition; result analysis of the determined
classes; best t selection. It was observed that the class denition methodology for the FMA⁺ system
obtained excellent results. It increased by 19.3, 21.53, and 31.3% for the percentage of success for subzones
1, 2, and 3, respectively, which implies this an important study for the successful implementation of FMA⁺
in other areas.
Keywords: FMA⁺; Wildfire; Statistics
Resumo
O objetivo deste estudo foi calcular a Fórmula Modicada de Monte Alegre (FMA⁺) e ajustar as classes de
risco de incêndio em áreas de orestas plantadas na costa norte-central do estado do Espírito Santo e na
costa sul do estado da Bahia. A metodologia utilizada incluiu seis etapas: cálculo de risco; desenvolvimento
de planilhas de acordo com a ocorrência, ou não, de incêndios orestais; desenvolvimento de planilhas de
acordo com a estação de incêndios orestais na região estudada; denição de classe de risco; análise de
resultados das classes determinadas; seleção de melhor ajuste. Observou-se que a metodologia de denição
de classe para o sistema FMA⁺ obteve excelentes resultados. Aumentou em 19,3; 21,53 e 31,3% para o
percentual de sucesso nas subzonas 1, 2 e 3, respectivamente, o que traduz em resultados este importante
estudo para a implementação bem-sucedida da FMA⁺ em outras áreas.
Palavras-chave: FMA⁺; Incêndios florestais; Estatística
I Engenheiro Florestal, Dr., Professor do Programa de Pós-graduação em Engenharia Florestal, Universidade Federal de Santa Maria, Cidade
Universitária, Av. Roraima, 1000, CEP 97105-900, Santa Maria (RS), Brasil. fernando.eugenio@ufsm.br (ORCID: 0000-0002-1148-1167)
II Agrônomo, Dr., Professor do Programa de Pós-Graduação em Ciências Florestais, Universidade Federal do Espírito Santo, Av. Governador
Lindemberg, 316, CEP 29550-000, Jerônimo Monteiro (ES), Brasil. mundogeomatica@yahoo.com.br (ORCID: 0000-0003-2617-9451)
III Bióloga, Professora agregada da Universidade de Barcelona, Diagonal, 643, CEP 08028, Barcelona, Espanha. bduguy@ub.edu (ORCID: 0000-0002-
2903-1981)
IV Engenheiro Florestal, Dr., Professor do Programa de Pós-Graduação em Ciências Florestais, Universidade Federal do Espírito Santo, Av.
Governador Lindemberg, 316, CEP 29550-000, Jerônimo Monteiro (ES), Brasil. pezzopane@pq.cnpq.br (ORCID: 0000-0003-0024-4016)
V Engenheiro Florestal, Mestrando do Programa de Pós-Graduação Solos e Nutrição de Plantas, Escola Superior de Agricultura “Luiz de Queiroz”,
Universidade de São Paulo, Avenida Pádua Dias, 11, CEP 13418-900, Piracicaba (SP), Brasil. cassiocarlette@hotmail.com (ORCID: 0000-0002-3564-
7440)
VI Engenheira Florestal, Dr., Pesquisadora Autônoma, Av. Governador Lindemberg, 316, CEP 29550-000, Jerônimo Monteiro (ES), Brasil. nssaito@
gmail.com (ORCID: 0000-0002-3329-7870)

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Introduction
Forest res are the result of complex interactions among vegetation, climate, topography,
and anthropogenic activities over time. However, local climatic conditions have a direct inuence
on their occurrence and spread, given that the intensity of a re and the speed by which it
advances are directly linked to relative air humidity, air temperature, and wind speed because
these aect the moisture content of the fuel; the amount of biomass, which is the main controller
of principal re characteristics; and the vegetation type (CHANG et al., 2015).
This relationship between meteorological variables (air temperature, precipitation,
relative humidity, wind speed, etc.) and forest res (occurrence, propagation, burned area, etc.)
has always been the object of research conducted by many researchers throughout the world.
However, the study of climatic variables to understand forest res is not recent. According
to Eugenio et al. (2019), during the last several decades this relationship has been studied by
several researchers, among which are the notable works of Flannigan and Harrington (1988);
Viegas, Viegas and Ferreira (1992); Vázquez and Moreno (1993); Viegas and Viegas (1994); Piñol.
Terradas anLloret (1998), Skinner et al. (1999); Diaz-Delgado (2000); Váquezand Moreno (2001);
Viegas et al. (2001); Duguy (2003); Viegas et al. (2004); Pereira et al. (2005); Krawchuket al. (2009);
Pausas andKeeley (2009); Bediaet al. (2012); Duguyet al. (2013); and San-Miguel-Ayanz, Moreno
and Camia (2013).
Therefore, because of their abilities to provide quantitative estimates of the possibility of
forest re occurrence, hazard indices based on meteorological data have become important tools
to evaluate the potential risk of regional res (HOLSTEN et al., 2013).
In 1972, Dr. Ronaldo Viana Soares developed the rst re risk index for Brazilian
conditions, the Monte Alegre Formula (FMA). From a simplistic view, it can be said that the
FMA is a cumulative index that uses as meteorological variables relative air humidity and
precipitation (NUNES; SOARES; BATISTA, 2006). José Renato Soares Nunes in 2005 added wind
speed, a factor of great importance for prevention and ghting forest res, thus developing the
Modied Monte Alegre Formula (FMA⁺). It was tested and approved for use in the region of
Telêmaco Borba, state of Paraná (NUNES; SOARES; BATISTA, 2006).
Since its creation, FMA⁺ has been used by several researchers and companies in Brazil
and is among the most used indices throughout the entire nation. Notable relevant studies are
those of Nunes, Soares and Batista (2006; 2009), Nunes et al. (2010), Borges et al. (2011), Pereira,
Batista and Soares (2012), Rodríguez et al. (2012), Souza, Casavecchia and Stangerlin (2012), White
et al. (2013), Soriano, Daniel and Santos (2015), and White, White and Ribeiro (2015). However,
several of these studies have a low percentage of success; the studies by White et al. (2013) and
White, White and Ribeiro (2015) obtained 38.64 and 36%, respectively, in areas with eucalyptus
plantations in the north coast of Bahia state. Borges et al. (2011) found values of success that
ranged between 51.54 and 56.47% in the same area of the present study.
It is important to stress that to use of FMA⁺ in the entire state of Paraná is feasible,
Nunes, Soares and Batista (2009) developed an FMA⁺ adjustment methodology, which is based
on the evaluation of the index performance in several regions of the state. However, the use of
this methodology in dierent states of Brazil has been occurring over the years without any
adjustment of its classes, which has led to the diculty of applying the methodology proposed
by Nunes, Soares and Batista (2009). This has led to low percentages of success in several studies
using FMA and; therefore, the use of other indices in areas outside the state of Paraná by
companies in the forest sector has been common.
Based on this assumption and considering the need to adjust the re risk classes provided
by the FMA⁺ for any area other than that in which it was developed, the objective of this study
was to calculate the FMA⁺ and adjust the wildre risk classes to areas of forests planted in the

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northern-central coast of the state of Espírito Santo and the southern coast of Bahia state.
Materials and methods
Study area
The study area extends from the northern-central coast of the state of Espírito Santo
to the southern coast of Bahia state, as described by Eugenio (2019) for the delimitation of the
area that was used a buer of 70 km from the coast, because, within this buer, is the region
that has the largest number of planted eucalyptus forests and all of the meteorological stations
of the forestry companies. The study area was divided into three climatic subzones delimited
according by Eugenio (2019). The occurrences of forest res and their climatic subzones are
shown in Figure 1.
Figure 1 – Study area and its climatic delimitations for forest res
Figura 1 – Área de estudo e a delimitação climática para os incêndios orestais
Source: Eugenio (2019)
For a better understanding of the methodology used, it was divided into six stages as
follows: stage 1 – risk calculation; stage 2 – spreadsheet development according to the occurrence,

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or not, of forest res; stage 3 –spreadsheet development according to the wildre season in the
study region; stage 4 – risk class denition; stage 5 – result analysis of the determined classes;
stage 6 – best t selection.
Stage 1 – Risk Calculation
The FMA⁺ was used for the daily calculation of the risk of occurrence of forest res,
according to equation 1, conceived by Nunes, Soares and Batista (2009), as follows in Equation
(1):
(1)
in which:
FMA+: Monte Alegre Altered Formula;
H: air relative humidity (%) measured at 13 o'clock;
n: number of days without rainfall greater than or equal to 13.0 mm;
V: wind speed in m/s, measured at 13 o'clock.
Because FMA⁺ is a cumulative index, regarding relative humidity, it is subject to
precipitation restrictions (Table 1).
Table 1 – FMA⁺ restrictions according to the amount of rain in the day and its
modications due to the air relative humidity (H) at 1 p.m
Tabela 1 – Restrições da FMA⁺ de acordo com a quantidade de chuva no dia e suas
modicações devido à umidade relativa do ar (H) às 13h
Rain in the day (mm) Modications
< 2.5 None
2.5 ˫ 5.0 Decrease 30% in the value of FMA + calculated on the day
before and add up (100 / H) of the day
5.0 ˫ 10 Decrease 60% in the value of FMA + calculated on the day
before and add (100 / H) of the day
10 ˫ 13 Decrease 80% in FMA + calculated on the day before and add
up (100 / H) of the day
≥ 13 Stop calculation (FMA + = 0), starting the next day.
Source: Nunes, Soares and Batista (2006), adapted by the author
Stage 2 – Spreadsheet development according to the occurrence, or not, of
forest res
The area of coverage of each meteorological station was delimited in the work of Eugenio
(2019). Given this, it was possible to identify the dates of wildlife occurrence during each season.
From the database of each meteorological station, separation of the days with and without forest
res was completed to obtain two new spreadsheets for each: those with the FMA+ values of the
days with and without wildre occurrence.
It is important to note that the data of with or without wildlife occurrence originates
from a forestry company spreadsheet that contains the date, time, area, cause, and geographical

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coordinates of each forest re occurrence within the study area during all the years studied;
therefore, they are the true eld data record of forest res.
Stage 3 – Spreadsheet development according to the wildre season in the
study region
Eugenio (2019) described that the study area has three climatic subzones (subzones 1, 2,
and 3). The author also states that each subzone has dierent wildre occurrence times as follows:
for subzone 1, season 1: December to March and season 2: August to October; for subzone 2,
season 1: January to March and season 2: August to October; and for subzone 3, season 1: January
and February and season 2: August to October.
Taking advantage of the spreadsheets generated during stage 2, the subzones were also
separated by the occurrence time to calculate the accuracy percentage and skill score test. This
culminated in the generation of nine spreadsheets, arranged as follows:
Spreadsheet 1: subzone 1 + days of season 1 WITH res + days of season 1 WITHOUT res;
Spreadsheet 2: subzone 1 + days of season 2 WITH res + days of season 1 season 2
WITHOUT res;
Spreadsheet 3: subzone 1 + total days WITH res + total days WITHOUT res;
Spreadsheet 4: subzone 2 + days of season 1 WITH res + days of season 1 WITHOUT res;
Spreadsheet 5: subzone 2 + days of season 2 WITH res + days of season 2 WITHOUT res;
Spreadsheet 6: subzone 2 + total days WITH res + total days WITHOUT res;
Spreadsheet 7: subzone 3 + days of season 1 WITH res + days of season 1 WITHOUT res;
Spreadsheet 8: subzone 3 + days of season 2 WITH res + days of season 2 WITHOUT res;
Spreadsheet 9: subzone 3 + total days WITH res + total days WITHOUT res.
Stage 4 – Risk class denition
The rst class methodology used was that conceived by the creator of the model (NUNES;
SOARES; BATISTA, 2006) as follows: Null=≤3.0; Small=3.1–8.0; Average=8.1–14.0; High=14.1–
24.0; and Very High=≥ 24.0.
With the predened number of classes, the stage for dening the limits of classes of the
FMA+ followed the subzones of the present study, there were two types of analyses conducted as
follows: denition by percentiles and logistic regression.
The analysis based on the denition by percentiles was obtaining the FMA+ values in
the percentiles of 20, 40, 60, 80, and 90 of the days during which forest res occurred. The class
values derived from the percentile analysis were described by the identiers (id.) A, C, E, G, I, K,
M, O, and Q.
The class denition by means of logistic regression was performed based on the regression
model described by Hosmer and Lemeshow (2000) as presented in Equation (2):
(2)
in which:
g(x) = β0 + β1 x1 + β2 x2 + ... + βi xi
P(y1 = 1): probability of occurrence of wildre;
x1: independent variable (FWI value);
βi: coecients expected by the maximum likelihood method.
The following probability values were used to determine the risk classes: 0.20, 0.40, 0.60,

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0.80, and 0.90. The class values derived from the logistic regression were described by the ids B,
D, F, H, J, L, N, P, and R.
Stage 5 – Results analysis of the determined classes
Aer performing the calculations and determining the values for each class, the re risk
behavior for the study area was obtained using the dierent methodologies.
To analyze the risk behavior based on the value of FMA+ in the dierent classes, a cross-
reference was conducted of the calculated risk and the dates on which forest res occurred, or
not. Skill Score (SS) and Percent Success (PS) methods were also used in the works of Sampaio
(1999), Nunes, Soares and Batista (2006), Borges et al. (2011), and Dimitrikoupolos, Bemmerzouk
and Mitsoupoloulos (2011).
The cross-risk analysis provided an estimate of the condence of each calculated risk
because it is based on the ratio of the dierence between the correctness of the prediction and
the expected number of hits, as well as the dierence between the number of days observed and
the number of days (Tables 2 and 3).
Table 2 – Contingency table
Tabela 2 – Tabela de contigência
Event Forest res Expected total
Observed Not observed
Wildre Expected a b N2 = a + b
Not expected c d N4 = c + d
Total observed N1 = a + c N3 = b + d N = a+b+c+d
Source: Sampaio (1999), adapted by the author
Table 3 – Calculations of the contingency table
Tabela 3 – Cálculos da tabela de contigência
Event Forest res Expected total
Observed Not observed
Wildre Expected a / (a+c) b / (b+d) 1
Not expected c / (a+c) d / (b+d) 1
Total observed 112
Source: Sampaio (1999), adapted by the author.
The equations for performing the calculations were, in Equations (3), (4), (5), (6) and (7):
N = a + b + c + d (3)
in which:
N: total number of observations;
a: number of days with occurrences of expected and observed res;

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b: number of days with occurrences of expected res and not observed;
c: number of days with occurrences of res not expected and observed; and
d: number of days with occurrences of res not expected and not observed.
Ga = a + d (4)
in which:
Ga: number of hits in the forecast.
Ha = N (1 – p )(1 – q) + Npq (5)
in which:
Ha: expected number of hits;
p = N1 / N: number of days with occurrences of expected and observed res;
q = N2 / N: number of days with occurrences of res anticipated and not observed;
N1: number of days with occurrences of res planned and observed plus number of days with occurrences of
res not expected and observed;
N2: number of days with occurrences of res anticipated and observed plus number of days with occurrences
of res anticipated and not observed;
N3: number of days with occurrences of res expected and not observed plus number of res days with
occurrences of unexpected and unobserved res;
N4: number of days with occurrences of res not expected and observed plus number of days with occurrences
of res not expected and not observed;
p: number of days with occurrences of res expected and observed plus number of occurrences of unexpected
and observed res occurring, divided by the total number of comments; and
q: number of days with occurrences of expected res and observed plus number of days with occurrences of
expected and unobserved res, divided by the total number of observations.
SS = (Ga – Ha) / (N – Ha) (6)
in which:
SS: skill score.
PS = (Ga / N) 100 (7)
in which:
PS: percentage of success.
Stage 6 - Best t selection
Class selection is a crucial stage for the correct use of a risk index. The rst selection was
made according to the original model classes. If the values of success and skill score do not agree
with those expected, one can choose from among the other classes tested in the ids from A to L.
The methods used in the present study consisted of the validation and choice of the
presented results via the percentages of success and the skill score value for each subzone.
Initially, normalization of the data of the percentage of success with and without res was
completed, in general. In addition, the skill score values were normalized within a scale ranging
from 0 to 100.
Aer value normalization, a hypothesis test was conducted using the Shapiro–Wilk test
to determine if the sample is or is not originating from a normal distribution. If H₀, the sample
originates from a normal distribution and if H₁, the sample does not originate from a normal
distribution.
To determine if the sample originate from a normal distribution, the Analysis of Variance
(ANOVA) was performed, which possesses as a hypothesis the equality between the averages of
two or more populations. If the F test is signicant, the Tukey–Kramer post-hoc test (signicance
level = 0.05) was completed to compare all the ids among each other. Given this, the highest
average value is the chosen id.

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However, if the sample did not present a normal distribution, Kruskall–Wallis
nonparametric analysis of variance was used and the null hypothesis was determined is the
equality between the categories; the ids in each subzone were assessed to a level of signicance
equal to 0.05 and 95% reliability intervals.
This methodology attempted to solve a dicult situation experienced in areas of forests
planted in the northern-central coast of Espírito Santo and the southern coast of Bahia, because,
of all the years used to dene this methodology, in this region approximately 92% of days were
without the occurrence of forest res and only 8% of days had forest res. In addition to this
factor, as reported by Eugenio (2019), the area has a history of illegally started res, thus reducing
the relationship between the variables and their responses in the model. All six stages used to
conduct the present methodology are shown in Figure 2.
Figure 2 – Flowchart of the six steps required to perform the methodology
Figura 2 – Fluxograma das seis etapas necessárias para executar a metodologia

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Source: Authors (2019)
Results and discussion
Aer the database preparation, the risks were calculated for all subzones and classied
using the classes proposed by Nunes, Soares and Batista (2009). The results found for the success
percentage of the days with and without re and the general and skill score tests are presented
in Table 4.
Table 4 – Results obtained by the success percentage test and skill score test for the class
values proposed by Nunes, Soares and Batista (2009)

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Tabela 4 – Resultados obtidos pelo teste de porcentagem de sucesso e teste de skill score para os
valores de classe propostos por Nunes, Soares and Batista (2009)
Subzone Sucesspercentage (%) Skill score
With wildre Without wildre Geral
187.36 47.08 51.88 0.1306
290.24 34.98 41.11 0.0779
392.41 37.26 40.64 0.0545
Source: Authors (2019)
As can be observed in Table 4, there was a good correlation for the days on which re
occurred, reaching 92.41% in subzone 3; however, when analyzing the days on which re did not,
good results were not obtained, the reason for which the overall success percentage was reduced.
The analysis of the values found by the skill score test reects this reduced accuracy because the
very low values - except in subzone 1. Therefore, there is a need to continue the methodology
because it is believed that better classes can be determined, according to the local database, and,
consequently, a better accuracy is obtained in the results of the percentage of general success
and skill score.
Table 5 portrays the results obtained using the dierent approaches described in the
methodology. Notably, all the classes originated using the percentile method have the same
percentages of analysis and the classes of those originated using the logistic regression following
their equation.
Analyzing Table 5, it is possible to identify a large dierence between the limit values
of the originating classes using the percentile method versus the classes from the logistic
regression. When analyzing the limit values of the "extreme" class obtained by percentiles, the
highest value was found in id G (FMA=78). This same value was surpassed by all the lower limits
of the "average" class obtained via logistic regression, with its lower value in id F (FMA=86).
Therefore, the lowest limit value of the percentile classes is less than the value considered
as the risk divisor of forest res of the classes dened by the logistic regression for the FMA⁺.
The analysis of the results found using the percentage of success and skill score test is shown in
Table 4.
Table 5 – Results found for each id followed by the percentage or equation used, with the
limit FMA⁺ values for the classes
Tabela 5 – Resultados encontrados para cada ID seguido da porcentagem ou equação utilizada,
com os valores limite de FMA⁺ para as classes

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Subzone id Porcentage / Equation FWI limit values for the classes
Low Moderate High Very high Extrem
1
A20%. 40%. 60% and 90% 0 – 10 10.1 – 17 17.1 – 26 26.1 – 56 >56
B1/[1+exp(−2.462+0.024×
FMA+)] 0 – 28 28.1 – 94 94.1 – 148 148.1 – 267 >267
C20%. 40%. 60% and 90% 0 – 13 13.1 – 20 20.1 – 30 30.1 – 65 >65
D1/[1+exp(−1.811+0.015×
FMA+)] 0 – 40 40.1 – 89 89.1 – 129 129.1 – 219 >219
E 20%. 40%. 60% and 90% 0 – 10 10.1 – 17 17.1 – 25 25.1 – 56 >56
F1/[1+exp(−2.180+0.020×
FMA+)] 0 – 45 45.1 – 86 86.1 – 120 120.1 – 194 >194
2
G 20%. 40%. 60% and 90% 0 – 14 14.1 – 23 23.1 – 35 35.1 – 78 >78
H1/[1+exp(−2.398+0.013×
FMA+)] 0 – 44 44.1 – 101 101.1 – 149 149.1 – 254 >254
I 20%. 40%. 60% and 90% 0 – 14 14.1 – 22 22.1 – 32 32.1 – 59 >59
J1/[1+exp(−2.125+0.017×
FMA+)] 0 – 126 126.1 – 323 323.1 – 485 485.1 – 843 >843
K 20%. 40%. 60% and 90% 0 – 12 12.1 – 20 20.1 – 30 30.1 – 64 >64
L1/[1+exp(−2.018+0.005×
FMA+)] 0 – 78 78.1 – 153 153.1 – 216 216.1 – 354 >354
3
M20%. 40%. 60% and 90% 0 – 14 14.1 – 23 23.1 – 35 35.1 – 63 >63
N1/[1+exp(−3.168+0.020×
FMA+)] 0 – 66 66.1 – 105 105.1 – 138 138.1 – 209 >209
O20%. 40%. 60% and 90% 0 – 14 14.1 – 23 23.1 – 34 34.1 – 60 >60
P1/[1+exp(−3.037+0.025×
FMA+)] 0 – 88 88.1 – 154 154.1 – 207 207.1 – 327 >327
Q 20%. 40%. 60% and 90% 0 – 14 14.1 – 22 22.1 – 31 31.1 – 59 >59
R1/[1+exp(−2.712+0.015×
FMA+)] 0 – 89 89.1 – 138 138.1 – 179 179.1 – 268 >268
Source: Authors (2019)
It is possible to predict—with the limit values of the classes—that the risk analysis
through logistic regression will encompass the highest number of FWI values in the low and
moderate classes, as opposed to the values obtained via percentile analysis. It can be said that for
the conditions of the present study, the logistic regression analysis is less sensitive to the lower
values of wildre risk and may overestimate low risk conditions, which may lead to a situation
in which the qualication of the risk presented is low, but it actually is a very high risk. This fact
is proven by the analysis of the results found using the percentage of success test and skill score
test, both demonstrated in Table 6.
Table 6 – Results obtained by the percentage of success test and skill score test for the

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values of class
Tabela 6 – Resultados obtidos pelo teste de porcentagem de sucesso e teste de skill score para os
valores da classe
Subzone Id. Porcentage of success (%) Skill score
With wild re With out wild re General
1
A60.29 65.30 64.35 0.1802
B0.91 97.92 79.61 0.0000
C 58.31 71.17 69.18 0.1998
D1.81 97.52 82.75 0.0000
E 61.39 72.50 71.18 0.1979
F 1.54 98.66 87.09 0.0032
2
G 59.83 63.17 62.64 0.1408
H3.16 98.66 83.56 0.0286
I 61.32 58.25 58.66 0.0979
J0.00 100.00 86.80 0.0000
K 61.17 64.18 63.85 0.1214
L 0.14 99.73 88.69 0.0000
3
M58.29 73.05 71.94 0.1346
N0.00 99.74 92.23 0.0000
O59.59 64.29 63.87 0.0970
P 0.59 99.80 90.95 0.0069
Q 58.90 70.74 70.01 0.1023
R0.42 99.73 93.63 0.0028
Source: Authors (2019)
Table 6 can be analyzed in a number of ways: by the percentage of success, that is,
percentage of correctness of the model for the days on which res occurred; for the days on
which res did not occur; a general analysis encompassing every day without res; or even by
the values obtained using the skill score test.
The ids originating from the logistic regression have the highest value overall success
percentages. It can be observed that the lowest value of assertiveness was obtained via logistic
regression was id B which was 79.61%; it exceeds by 7 percentage points the highest value
obtained using the percentile method.
Regarding the days with re, the days with the lowest correct value for the ids referring to
the percentile classes is always much higher than those of the logistic regression class, reaching
up to a 55 percentage point dierence - id M with 58.29% and id H with 3.16%. Notably, logistic
regression ids occurred that do not correctly identify any day with re, as in the case of ids N and
J, with a 0.00% accuracy.
There is also a dierence between the values determined in the skill score test when
comparing the dierent methods for the class boundaries, the lowest percentile value being id
O, with 0.0970. These values were greater than the highest value found in the logistic regression

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classes, with its highest value for id H of 0.0286. There are ids with values equal to zero originating
from logistic regression, as in the case of ids B, D, J, L, and N, which reinforces the importance of
class delimitation according to the results found in the study area, in which it was applied using
the formula to calculate the probability of wildre risk.
This preliminary analysis is a fundamental part in understanding the behavior of the
classes and their limits against a population of values of wildre risk because, in a simplistic
analysis, the percentage of overall success would lead to failure because, as previously reported,
there are cases in which a high accuracy in the general percentage does not show an accuracy for
those days on which re occurred.
In the case of id J, in which 100% of the days without re were identied and it had
an overall success rate of 86.80%, 0% of days with wildre were accurately projected and it
had a skill score of 0.0000, though. If a researcher has used this model because it had a high
overall percentage of correctness, he/she could also conclude that no model of re risk would be
necessary because of an assumption that there will be no re on any day, which translates into
an error of 12.60% of the days; however, the researcher would be accurate 87.40% of the time for
the number of days on which there was no re.
Nevertheless, the opposite—high accuracy on days with re—leads to the understanding
that it a wildre will occur every day. In this case, the error rate would be approximately 90% of
the days. Considering such issues, it is understood there is a need for a statistical evaluation with
data standardization which is incontestable to infer which model to use.
Aer analyzing the results in a visual manner, statistical tests were performed to verify
the existence, or not, of dierences between the results obtained using the classes of dierent
ids.
Initially, the normalization of the success percentage data with and without re and
the general and skill score values were normalized to a scale that ranges between 0 and 100.
Following value normalization, a hypothesis test was performed using the Shapiro–Wilk test,
in which H₀ is a sample originating from a normal distribution and H₁ is a sample that does not
originate from a normal distribution (Table 7).
As can be observed in Table 7, the ids presented values higher than 0.05; thus, it is
acceptable to have a null hypothesis.
Together with the data that presented a normal distribution for both subzones, a
parametric test of ANOVA was conducted, which has as a hypothesis the equality between the
averages of two or more populations; in the present case, the equality between the normalized
values for each id. As the F test was signicant, the Tukey–Kramer post-hoc test was used to
compare all the ids. The test results are shown in Table 5.
The Tukey–Kramer test was performed at a signicance level of 0.05 and a 95% condence
interval. For both subzones, the null hypothesis was not rejected; that is, the distribution of the
normalized values is the same among the dierent identiers for each subzone. Therefore, the
choice of the best identier for each subzone was based on the highest average found. As can be
seen in Table 5, the highest average value for subzone 1 was id E, with an average value equal to
24.06; for subzone 2, it was chosen id G, with an average value of 23.90; and for subzone 3, it was
id M with an average value equal to 25.32.
Table 7 – Results found using the Shapiro–Wilk and Tukey–Kramer test for the dierent
ids
Tabela 7 – Resultados encontrados no teste Shapiro–Wilke Tukey–Kramer para os diferentes ids
Subzone Season Method Id. Shapiro-Wilk Tukey-Kramer

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1
1Percentile A0.095 22.72
Logistic regression B 0.077 9.37
2Percentile C0.129 23.85
Logistic regression D 0.070 9.64
Total Percentile E 0.064 24.36
Logistic regression F 0.055 8.45
2
1Percentile G 0.155 23.90
Logistic regression H 0.383 12.06
2Percentile I 0.379 20.87
Logistic regression J0.051 10.03
Total Percentile K 0.092 22.96
Logistic regression L 0.054 10.05
3
1Percentile M 0.200 25.32
Logistic regression N 0.062 8.34
2Percentile O0.207 21.91
Logistic regression P0.081 10.21
Total
Percentile Q 0.137 22.84
Logistic regression R 0.057 9.23
Source: Authors (2019)
When analyzing the ids, the same result originates from the percentile analysis of all the
days on which forest res occurred in subzone 1; their accuracy for the days on which forest
res occurred was 61.39%, and for the days on which forest res did not occur, it was 72.50%.
Its success percentage was equal to 71.18% and its skill score was 0.1979. For subzones 2 and 3,
ids G and M were chosen, both from season 1, with 59.83 and 58.29% accuracy of days on which
re occurred; 63.17 and 73.05% accuracy on days on which res did not occur; 62.24 and 71.94%
values for success percentage; and skill score test values of 0.1408 and 0.1366, respectively.
The variation in values of the skill score test, among the dierent identiers tested, are
shown in Figure 3.
There is a visual dierence between the ids: they can be divided into two groups for each
subzone. The groups derived from the percentile methodology—A, C, and E; G, I, and K; and M,
O, and Q—with values higher than those found via logistic regression—and B, D, and F; H, J, and
L; and N, P, and R—which have the lowest values.
In relation to the skill score test, in both subzones the results found in the present study
are higher than those found by Nunes, Soares and Batista (2006) and Nunes et al. (2010) for the
forest district of Monte Alegre in the municipality of Telêmaco Borba, state of Paraná, Brazil; a
value of 0.11165 for the skill score test was obtained.
Figure 3 – Skill score values between the dierent identiers (ids) tested, highlighting the
ids chosen for subzones 1, 2 and 3
Figura 3 – Valores de skill-score entre os diferentes identicadores (ids) testados, destacando os
ids escolhidos para as subzonas 1, 2 e 3

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Ci. Fl., Santa Maria, v. 30, n. 4, p. 1085-1102, out./dez. 2020
Source: Authors (2019)
White et al. (2013), when evaluating FMA⁺ in areas of eucalyptus plantations on the
northern coast of Bahia state from January 1st, 2002, to December 31st, 2009, obtained a skill
score equal to 0.059. White, White and Ribeiro (2015), for the period between January 1st, 2002,
and December 31st, 2012, obtained a skill score equal to 0.05. Rodríguez et al. (2012) evaluated the
performance of wildre risk indices for areas of the Macujire forestry company, in Cuba, during
the period between January, 2006, and December, 2011, and obtained using FMA⁺ as skill score
test of 0.0737.
The results of the present study were slightly lower when compared to those found by
Borges et al. (2011), who conducted a study to verify the performance of some re risk indices in
eucalyptus plantations in the northern region of Espírito Santo state between the years 2003 and
2004 and obtained skill score values ranging from 0.1626 to 0.2055.
The variations in the values of the percentage of success among the dierent identiers
tested are shown in Figure 4.
A visual dierence between the identiers is apparent: they can be grouped into two
groups for each subzone. The groups derived from the percentile methodology (A, C, and E; G, I,
and K; and M, O, and Q), with values higher than those found via logistic regression, (B, D, and
F; H, J, and L; and N, P, and R), which have the lowest values for the percentage of global success.
In relation to the percentage of success obtained, for both subzones the results found
in the present study are superior to those found by Nunes, Soares and Batista (2006) and Nunes
et al. (2010), which obtained a value of 55.64%. Souza (2014) obtained 63.53% in a study of the
percentage of success in the municipality of Lages, in Santa Catarina state, higher only than that
found in subzone 2 of the present study. Rodríguez et al. (2012), when working with FMA⁺ for
areas of a forest company in Cuba, obtained 57.10%, which is a lower value than that found in
both subzones of the present study.
Borges et al. (2011) obtained values of success percentage that ranged between 51.54 and
56.47%, less than the value found in the present study of 68.45% on average.
However, for re occurrences in the Serra de Itabaiana National Park, a value of 48%
was obtained, which was less than that found in the subzones of the present study. Borges et al.
(2011) obtained values of success percentage that ranged between 51.54 and 56.47%, less than
those in the present study, which had an average of 68.45%. White et al. (2013) and White, White
and Ribeiro (2015) obtained 38.64% and 36%, respectively, values that were much lower than
those found in the present study for the percentage of FMA⁺ success in areas with eucalyptus
plantations in the northern coast of Bahia.

Eugenio, F. C.; Santos, A. R.; Pedra, B. D.;
Pezzopane, J. E. M.; Thiengo, C. C.; Saito, N. S. 1100
Ci. Fl., Santa Maria, v. 30, n. 4, p. 1085-1102, out./dez. 2020
Figure 4 – Percentage success values between the dierent identiers (ids) tested,
highlighting the chosen ids for subzone 1 (id E), for subzone 2 (id G), and for subzone 3 (id
M)
Figura 4 – Valores da porcentagem de sucesso entre os diferentes identicadores (ids) testados,
destacando os ids escolhidos para a subzona 1 (id E), para a subzona 2 (id G) e para a subzona 3
(id M)
Source: Authors (2019)
The average success rate found in the present study was higher than most of the previous
studies analyzed; however, to also verify the methodology described in Nunes, Soares and Batista
(2009), the decreasing curve in relation to the risks was analyzed.
Nunes, Soares and Batista (2009) reported that the number of days expected in each risk
class should have an inverse relationship with the risk class in such a manner that the higher the
risk class, the lower the number of days expected for it.
Therefore, the analysis completed with the data obtained by means of the id classes E, G,
and M for subzones 1, 2, and 3, respectively. For both subzones, there is an inverse relationship
between the number of days expected and the risk classes, with the class of higher risk having
the least expected number of days. The R² values for the subzones were 0.87, 0.75, and 0.90,
respectively, originating from a decreasing exponential function, meeting that proposed by the
FMA⁺ author.
As reported by Nunes et al. (2010), the observed mismatch in wildre risk is a factor
that interferes with its performance; this mismatch is probably caused by the change in rainfall
regimes and, consequently, of relative humidity over time. Therefore, to avoid the use of an
unsafe risk index, which may lead to mistaken decisions regarding wildre prevention and
control procedures, a prior adjustment is necessary.
Hence, the adjustment of the limit values of the classes performed by the presented
methodology is equivalent to a substantial gain when compared to the classes of the origin of
the index presented in Table 2, which has an average overall success percentage of 44.54%; it
increases to 68 and 59%. As observed in the present study, higher values were obtained for the
success percentage and skill score test when compared to the original values found in the index
development.
It is believed that numerous works could or can be improved by a simple study of the
correction of the limit values of classes in previous use of the FMA⁺ in study areas other than
that of the origin of risk.

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Ci. Fl., Santa Maria, v. 30, n. 4, p. 1085-1102, out./dez. 2020
Conclusions
The percentage of success increased by 19.3, 21.53, and 31.3% for subzones 1, 2, and 3,
respectively, when compared to the original method.
Logistic regression analysis is less sensitive to lower values and can overestimate low-
risk conditions, which may lead to a situation where the risk rating is low, while the risk is
actually very high.
The methodology proposed for the test of classes was ecient and allowed an analysis
of the values obtained for the classes, making it possible to perform the analysis of times with a
greater wildre occurrence and the total data set.
It was observed that the application of the percentiles for the development of limits for
new classes resulted in a greater index accuracy for the study subzones.
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