Previsão e Modelagem das Ocorrências de Incêndios no Pantanal

Prediction and Modeling of Forest Fires in the Pantanal

Resumo

As queimadas e incêndios descontrolados que ocorrem no Pantanal causam grandes prejuízos à fauna e flora locais. A previsão desses eventos é de grande importância por possibilitar que as catástrofes no ecossistema do Pantanal sejam amenizadas ou, até mesmo, evitadas. Tendo em vista que a prevenção contra incêndios deve ser constante, a identificação de focos de queimadas é essencial para uma intervenção imediata. Este estudo teve como objetivo avaliar as ocorrências de queimadas e incêndios no Pantanal Sul-Mato-Grossense, associadas às variáveis meteorológicas e realizar uma modelagem de previsão. As variáveis envolvidas nesse processo foram extraídas da base de dados do Centro de Previsão de Tempo e Estudos Climáticos do Instituto Nacional de Pesquisas Espaciais (INPE) e do banco de dados meteorológicos para ensino e pesquisa do Instituto Nacional de Meteorologia (INMET). Foram observadas que a temperatura, umidade relativa e radiação solar, possuem um relacionamento estreito com a ocorrência dos focos e as correlações resultantes foram satisfatórias para a aplicação das modelagens de previsão. A técnica de Regressão Linear Múltipla apresentou 41% de ajustamento e a técnica de Análise Auto-regressiva Integrada de Médias Móveis apresentou ajustamento de 66,5% e desempenho geral de 68,4%, tornando-a a metodologia mais recomendada para a previsão.

Palavras-chave:
monitoramento ambiental; bioma pantanal; prevenção de queimadas; previsão de fogo

Abstract

Uncontrolled fire points and forest fires in the Pantanal cause great damage to local flora and fauna. The prediction of these events is of paramount importance as it may mitigate or even avoid disasters in the Pantanal ecosystem. Given that fire prevention should be constant, the identification of fire foci is essential for immediate intervention. The objective of this study was to evaluate the forest fires in the Pantanal of Mato Grosso do Sul associated with the meteorological variables and to perform a forecast modeling. The environmental variables involved in the process were provided by the database of the Center for Weather Forecasting and Climate Studies of the National Institute for Space Research (INPE) and from the meteorological database for teaching and research of the National Institute of Meteorology (INMET). A close relationship was observed between the meteorological variables temperature, relative humidity and solar radiation and the occurrence of foci and the resulting correlations were satisfactory for the application of forecasting models. The Multiple Linear Regression technique presented fit of 41% and the Integrated Self-Regressive Analysis of Moving Average technique, 66.5%, and a general performance of 68.4%, thus making the latter the most recommended methodology for forecasting.

Keywords:
environmental monitoring; pantanal biome; prevention of fire points; fire forecast

1. Introduction

The occurrence of forest fires in the Pantanal of Mato Grosso do Sul is a serious threat to the conservation of the local biodiversity and influence the climate of this important biome, causing serious consequences to the maintenance of ecological processes, with results that affect human permanence in this natural habitat.

The main causes of forest fires and fire points in the Pantanal are: incorrect use of fire for land-clearing; renovation of pastures for extensive agriculture; pioneering work; hunting; pest control; coal production; and human beings neglect (Fiedler et al., 2006).

For the most part, fire points and forest fires have anthropogenic causes (Trejo, 2008) and, in the drought season, there are favorable conditions for them to propagate in great magnitude, as climatic factors such as high temperatures, wind and low relative humidity of air potentiate their occurrence, since drier air causes increased evapotranspiration of plants, favors greater performance of solar radiation on the earth’s surface, which, in turn, raises air temperature, thus creating an environment that is easily conducive to the combustion process (Deppe et al., 2004; Magi et al., 2012).

Fire points and forest fires occurs mostly between July and November, usually in the areas of savannah (cerrado) and Pantanal biome. Studies on the elemental composition of the aerosol particles resulting from fires show that the emission of black-carbon during the dry season exudes soot from combustion, associated with elements known as burner tracer, for example, Sulphur (S), Potassium (K), Chlorine (Cl), Calcium (Ca) and Zinc (Zn) (Nogueira et al., 2014, Nogueira e Santos 2015, Artaxo et al., 2006).

The damages caused by the burning processes in the various components of the biome are: i) in the vegetation, native species are lost; a decrease in the age of plants and trees is seen; plants are transformed for fire adaptation; a reduction of resistance of plant species is observed, as well as scarring, insect and fungal attacks, outbreaks and attacks of pests and diseases; ii) in the soil, organic layers are destroyed, exposed and weakened; landslides and erosion occur; changes in physical properties (porosity and water penetrability) are seen; iii) in the fauna, death of animals occur, nests are destroyed and habitats are modified (animals migrate in search of food and shelter); iv) in the properties, houses, constructions, vehicles, machinery and various equipment are destroyed; v) in human life, respiratory problems arise on account of the air pollution generated, road accidents occur caused by the smoke on the runway, people involved in fire-fighting die (Longo e Dias, 2005; Pereira et al., 2012; Soares et al., 2009; Silva, 2014).

In view of the great damage caused by the combustion process in the Pantanal biome, the forecast, control and monitoring of these events are of great interest to the competent authorities and to the Pantanal man. From this perspective, determining the origin of fire points in the Pantanal, the risks and the time of occurrence poses a challenge that has to be faced when conservation or management plans are created.

In order to avoid the major consequences of fire points and forest fires, it is necessary to manage them with specific and preventive actions. The first ones should be developed within each property and consists of: identifying the areas to be burnt; opening firebreaks whose width depends on the height of the vegetation to be burnt; setting the fire against the wind direction, counting on equipment required for firefighting (flame arresters, backpack fire pumps and water suction pumps); and keeping watch throughout the burning time.

The preventive actions consist of building monitoring networks for fire forecast. Brazil invests in technologies that allow monitoring and controlling heat sources in record time, which represents great help in fighting the approximately 300,000 fire foci reported annually (Granemann e Carneiro, 2009).

According to Silva (2014), the most efficient and less costly way to face the problem in countries with large territorial extension like Brazil is to monitor fire points and forest fires by means of satellite orbital images through the remote sensor process, which allows detecting and spotting fire foci in real time.

Other tools that can be used to predict fire foci are the techniques of multivariate analysis of time series, through which it is possible to predict the occurrence of the phenomenon from a mass of data about the values of some meteorological variables that influence the occurrence of fires and the number of foci.

Thus the objective of this work was to use the concepts of Multiple Linear Regression (MLP) and Auto-Regressive Integrated Moving Averages (ARIMA) to determine a mathematical modeling for predicting the number of fire foci in the Pantanal of Mato Grosso do Sul biome, taking into account the measurement levels of a series of meteorological variables related to the fire points and the influence of climatic factors correlated with the probability of occurring a combustion process.

2. Material and Methods

2.1. Study area

Located in the Upper Paraguay River Basin, in west-central Brazil, on the banks of the Paraguay River and bordering with Bolivia, Corumbá is the third largest city in the state of Mato Grosso do Sul, with about 104,000 inhabitants. It is the states largest county in territorial extension, with approximately 65,000 km²; 95% of which is part of the Pantanal biome (Ibge, 2016).

Corumbá lies between coordinates 19°00’32” S and 57°39’10” W, with an altitude of 118 m above sea level. According to Koppen, whose system is based on thermal and rainfall regimes and on the distribution of plant associations, Corumbás climate is classified as Aw (tropical humid mega thermal), that is, high-altitude tropical climate with dry winter and hot and wet summer (Soriano, 2007).

According to the State Secretary for Environment and Economic Development of Mato Grosso do Sul (SEMADE), and to the city characterization found at RADAMBRASIL, Corumbá is divided into three geomorphological regions: the Pantanal of Mato Grosso, the Upper Paraguay Depression, and the region of Bodoquena and Morrarias of Urucum-Amolar (Brasil, 1982; Imasul, 2016).

The predominant vegetation coverage is the typical Pantanal Cerrado (savannah), the Cerrado Park and the Open Arboreal Cerrado. In higher sites, forested areas are seen, and the Chaco vegetation is present southwards; the lower areas are covered by carandá (Copernicia alba) and paratudo (Tabebuia aurea) trees (Brasil, 1982; Imasul, 2016).

The criteria used in the delimitation of the study region took into account the aspects related to the areas with vegetation that produces dry mass with forest fire risks and that are representative of the Pantanal biome (Sobrinho et al., 2010).

2.2. Data collection

The climatological and meteorological variables analyzed were extracted from the geographic information system of the meteorological database for teaching and research of the National Institute of Meteorology (INMET), through collection station 83552 (19°00’36’’ S e 57°38’60’’ W), and collection platform database 31949 (19°01’19.2’’ S e 57°39’7.2’’ W), available at the Center for Weather Forecasting and Climate Studies of the National Institute of Space Research (CEPETEC - INPE) in a time series from 2005 to 2015 (Inmet, 2016; Inpe, 2016).

Twenty-four daily measurements of each variable were used, available on an hour basis, constituting a mass of data with 1,900,800 records for the whole time series from January to December, 2005-2015. For the July-November period (JASON), 792,000 records were used in the same series.

The data of the environmental variable number of foci were obtained from the Image Generation Division (DGI) of the National Institute of Space Research (INPE), that collects and processes the images of reference satellites of the National Oceanic Atmospheric Administration (NOAA-12) series (from 2005 to 2007) and the National Aeronautics and Space Administration - NASA AQUA MT (from 2008 to 2015), respectively using the Advanced Very High Resolution Radiometer (AVHRR) and the Moderate Resolution Imaging Spectroradiometer (MODIS) sensors. The pieces of information have the same pattern of time sampling and detection, the time of passage at the point of the Earth is the same over the years and the data are considered to be free of false detections that the reflections of the sun may cause on the Earth’s surface. Daily measurements were used hourly for the counting of detected foci without overlapping, with all the satellites that scan in the thermal range of 4 μm for the evaluation of the series seasonality and the checking of the period of most occurrences of foci. Later these data were filtered using only the reference satellite data for the application of multivariate methods of time series forecast, because they presented lower coefficients of variation.

The variables selected for the analysis of the correlation with the number of foci (N) were: Instant Air Temperature (°C) (T); Maximum Air Temperature (°C) (T_Max); Minimum Air Temperature (°C) (T_Min); Soil Temperature (°C) at 100, 200 and 400 mm (T_{S100, 200 and 400}); Rainfall (mm) P; Relative Humidity (%) (H_Rel); Absolute Humidity (%) (H_Abs); Wind Speed (m/s) at 10 meters (S_10m); Atmospheric Pressure (mb) (P_Atm); Accumulated Solar Radiation (MJ/m³) (R); Soil Water Count (m³) 100 mm, 200 mm and 400 mm (W_S100,200,400) and Vegetation (typology according to the IGBP - NASA data).

Air temperature is a measure of the average kinetic energy of molecules or atoms. The instantaneous air temperature was obtained by official meteorological stations at a height between 1,25 m and 2,00 m and 10 m high from soil measured hourly, and the average daily value was estimated by the compensated temperature range, given by T = (2.t₀₀ + t₁₂ + T_max + T_min)/5, where t₀₀ and t₁₂ are the temperatures observed at 00 h and 12 h Greenwich Mean Time (GMT); the maximum and minimum extreme temperatures were obtained for each interval of 24 h with the records of the maximum and minimum values of the daily series.

The soil temperature has a thermal regime determined by the heating of the surface by the solar radiation and transported to its interior by conduction of sensible heat; this heat flow depends on the thermal conductivity of the soil, specific heat, emissivity, type of soil, vegetation cover, solar irradiance, air temperature, wind, rainfall and topography. The measurements were made at depths of 100 mm, 200 mm and 400 mm, where significant variations in soil temperature occur.

The absolute humidity is given by the quotient between the mass of water vapor and the volume of humid air; it represents the vapor concentration. The relative humidity of humid air is provided by the quotient between the partial pressure of the vapor and the saturation pressure at a given temperature; it represents the fraction of the maximum possible moisture that is already filled. The humidity values were obtained from the official meteorological stations.

Solar radiation (or global radiation) is short electromagnetic waves emitted by the sun, responsible for terrestrial heating, given by the amount of energy radiated by the sun for 24 h and absorbed in the atmosphere after the same period. It was collected from the INPE database by means of satellites and systematically validated on the surface.

The soil water count is provided by the amount of water stored in the soil in one cubic meter and was collected in the database for depths of 100 mm, 200 mm and 400 mm, where the main water changes in the plant roots occur. The precipitation is expressed by the thickness of the water layer that would form on a flat, impermeable horizontal surface in a one-square meter area.

Wind speed is the most variable meteorological parameter for fire propagation; the faster it is, the greater the fire propagation, as the oxygen present in the combustion area is renewed and the area of ??contact between fuel and high temperature of combustion increases. It was collected at 10 m in height because of changes resulting from the spatial variability of the studied ecosystem.

2.3. Techniques of multivariate analysis

2.3.1. Multiple Linear Regression Analysis – MLR

The Multiple Linear Regression technique establishes a relation between a dependent variable and several independent variables. The General Linear Model is given by Eq. (1) when applied to a sample size “n” for a total of observations “i” (Hair et al., 2005; Levine et al., 2005).

(1) $$y_i={\text{β}}_0+{\text{β}}_{\text{1}}{x}_{1i}+{\text{β}}_{\text{2}}{x}_{2i}+\Lambda +{\text{β}}_n{x}_{ni}+{\text{ε}}_i$$

where: y_i is the dependent variable, also called response, i = 1, 2, ..., n; β₀ is the intercept or variable independent term; β_k is the y inclination in relation to variable x_k (k = 1, 2,... , n), keeping variables x₁, x₂,... , x_k-1 constant; ε_i is the random error in y_i.

The application of this model requires ${\text{ε}}_i\approx N\left(0,{\sigma }^2\right)$, that is, that the errors of observations i be independent and have a Gaussian distribution with a mean of zero and constant variance. Furthermore, it is necessary to use the analysis of variance of regression to check whether the fit of regression does exist, and to verify that the models general performance is suitable.

RLM modeling was applied using the meteorological variables that showed the greatest significance in correlation with the number of foci, namely maximum temperature, relative humidity and solar radiation. The variable that represents the logarithm of the number of foci (N) was introduced as a dependent variable and the others (T, U, R) were introduced as independent variables. For the correlation analyses and MLR modeling, 24 daily measurements of each variable were used. The base-10 logarithm was applied in the number of foci to make the series more homogeneous. RLM models were obtained using IBM-SPSS software in stepwise mode and 95% confidence level.

2.3.2. Autoregressive Integrated Moving Average Technique - ARIMA

The ARIMA technique is a sophisticated Box-Jenkins method for time series analysis using the correlations among the observations of data in different moments. It performs better than the smoothing methods when the series is relatively long and steady, and can describe three classes of processes: stationary linear, non-stationary linear and long-memory processes (Morettin e Toloi, 2006).

The ARIMA models (p, d, q) are d times “differentiated” from the original series; they have p autoregressive parameters and q parameters of moving averages. The differentiation order d is the number of differences required to turn a non-stationary series into a stationary one; it is used to remove the effects of tendencies. The number of autoregressive orders p specifies which previous values of series will be used to predict the current values; and the number of orders of moving averages q specifies how the deviations of average of series for previous values are used to predict the current values (Espinosa et al., 2010; Vieira et al., 2012).

The generic form of modeling is presented by Eq. (2) (Morettin e Toloi, 2006).

(2) $${\left(1-B\right)}^d\text{ϕ}\left(B\right)y_t=\text{θ}\left(B\right){\text{ε}}_t$$

where: φ(B) and θ(B) are the autoregressive and moving average operators; y_t is the value of y at a given time t; ε_t is the uncorrelated random error, with mean zero and constant variance (white noise); B is the lagged operator and d is the number of the series differentiation.

To apply this method, the following steps were followed: (i) preparation of historical data; (ii) determination of stationarity and verification of seasonality in the series; (iii) differentiation until reaching stationarity; (iv) verification of the obtained model; and (v) reach of the forecast model (Espinosa et al., 2010; Moretin e Toloi, 2006).

In order to compare the modeling of the two systems, the same variables of RLM and ARIMA were used. The number of foci was introduced as a dependent variable and the meteorological variables (temperature, humidity and radiation) were introduced as independent variables. Twenty four daily measurements of each variable were used to compose the ARIMA forecast system. For the application of this method, the time series predictor of the IBM-SPSS software was used in the expert modeler mode with the forecast after the last case under analysis and up to five steps ahead.

2.3.3. Statistical analyses

The statistical analyses applied to the variables were: a) Pearson correlation of the independent variables and a dependent variable, in this case the number of foci; b) Analysis of Variance (ANOVA); c) Statistics F; d) Durbin-Watson test; e) analysis of the Variance Inflation Factor ; f) Bayesian Information Criterion (BIC); g) analysis of the functions of Autocorrelation of Residuals; h) Error Analysis: root mean square error (RMSE), Mean Absolute Percentage Error (MAPE) and Mean Absolute Error (MAE); i) Bias; j) Accuracy factor D (Levine et al., 2005).

The modeling equation was obtained by applying the MLR method using the variables that showed the greatest significance. The estimated values were obtained by the ARIMA method and compared in both models.

For the analysis of descriptive statistics, correlations and MLR and ARIMA models, the IBM - SPSS data mining program was used. The accuracy of measurements was determined by the calculations of the MAPE associated with the fit parameters, p-value and R², and the model validation was evaluated by the Bayesian information criterion.

The fit of the models was obtained through the analysis of R², p-value, F-ratio, Durbin-Watson statistics, Analysis of Variance (ANOVA) and analysis of model parameters. The analyses of residuals and bias were performed by the t-test, Analysis of Variance and Distribution F.

It should be noted that 24 daily measurements (hourly measurements) of each independent variable were made, and from the daily compensated mean of each meteorological variable, a comparison was drawn with the daily measurement of the reference satellite for regression analysis and ARIMA.

3. Results and Discussion

A descriptive analysis of data was initially performed to identify the years and months with the highest incidence of heat foci in the Pantanal biome of Corumbá - MS. To this aim, tables, graphs, measures of centrality (mean and median), and measures of variability (standard deviation and coefficient of variation) were needed.

Table 1 shows the distribution of foci, the monthly averages, the standard deviations and the corresponding coefficients of variation for the series analyzed, from January to December, in the 2005-2015 period.

Table 1
Monthly statistics of the total number of foci, obtained from all satellites operating on the 4 μm thermal band (NOAA- 12; NOAA-15; NOAA-16; NOAA-18; NOAA-19; NASA AQUA M-T; GOES-12; GOES-13 and MSG-2) for the total scanning of 24 hourly measurements per day from 2005 to 2015 in Corumbá (MS).

Years	Month
	JAN	FEB	MAR	APR	MAY	JUN	JUL	AUG	SEP	OCT	NOV	DEC
2005	4	176	142	212	538	635	2272	12164	4608	1110	402	114
2006	102	109	44	9	160	64	257	812	1198	318	701	13
2007	9	20	69	88	67	120	184	2485	5327	1123	434	84
2008	48	26	44	56	20	6	65	617	2837	909	615	1054
2009	898	450	305	1098	2840	668	947	1651	2590	3146	1364	162
2010	50	174	239	143	87	310	1074	2097	4073	1082	957	1976
2011	228	32	5	9	51	68	94	270	887	873	2073	3770
2012	1155	506	537	464	572	228	1947	17446	8684	3998	839	514
2013	661	286	523	94	140	11	159	697	2295	1328	1596	646
2014	275	339	52	317	25	68	235	421	604	1461	597	66
2015	406	357	229	211	356	1094	1201	6154	7347	2998	1663	3590
Mean	349	225	199	246	441	297	767	4074	3677	1668	1022	1090
SD*	393	174	190	314	820	353	786	5681	2635	1163	564	1406
CV*(%)	113	77	95	128	186	119	102	139	72	70	55	129

• ^*
  SD: Standard Deviation; CV: Coefficient of Variation.

According to Table 1, the monthly averages in the period 2005-2015 presented considerable increase from July on, with a peak in August and September, reaching maximum values (4074 and 3677 foci, respectively). The standard deviations and hence the coefficients of variation present high values, indicating a large heterogeneity of data. This is understandable because, in the first semester, few fire foci occurred whereas in the second, the dry season, a considerable increase was observed.

The period selected for the application of RLM and ARIMA forecasting techniques was, therefore, restricted to the months of July, August, September, October and November of each year, known as the JASON (the first letter of each month) period that corresponds to the period with the highest concentration of foci events. For the analysis of time series, a cut was made in the number of foci detected only by the reference satellites NOAA-12 and NASA AQUA MT because they presented polar orbit, which generates data that can be statistically analyzed for the same regions along the years with minimized errors and corrected atmospheric effects.

For performing the regression analysis, the base-10 logarithmic transformation was applied on the number of foci to stabilize the variance because of the great variability of these data, since the forecasts must be characterized by the accuracy of results, the simplicity of methods employed and the statistical reliability of the models used to generate predictions.

Table 2 shows the results of the linear correlation between the variable related to the fire foci and its meteorological predictor variables.

Table 2
Pearson’s correlation coefficient test (r) between the occurrences of fire foci and the studied environmental variables in the period 2005-2015 in Corumbá (MS).

Variables*	r	Variables*	r
TMax (°C)	0.383	W100 (m3)	-0.041
T (°C)	0.092	W200 (m3)	-0.144
TMin (°C)	0.104	W400 (m3)	-0.038
R (MJ/m2)	0.310	DMax (°NV)	-0.080
TS100 (°C)	0.183	D (°NV)	-0.090
TS200 (°C)	0.165	P (mm)	-0.085
TS400 (°C)	0.013	PAtm (mB)	-0.019
S10 (m/s)	0.114	HRel (%)	-0.564
SMax (m/s)	0.067	HAbs (%)	0.037

• ^*
  Were: Instant Air Temperature (T); Maximum Air Temperature (T_Max); Minimum Air Temperature (T_Min); Soil Temperature at 100, 200 and 400 mm (T_{S 100, 200 and 400}); Rainfall P; Relative Humidity (H_Rel); Absolute Humidity (H_Abs); Wind Speed at 10 meters (S₁₀); Atmospheric Pressure (P_Atm); Accumulated Solar Radiation (R); Soil Water Count at 100 mm, 200 mm and 400 mm (W_100,200,400).

The negative values presented by correlations (r) mean that the lower the value of the climate element, the higher the possibility of fire occurrences. However, if the value of r is positive, the higher the value of the parameter, the lower the probability of occurring fire foci.

The meteorological variables that favor most the occurrence of foci according to the correlation analysis for the application of the RLM and ARIMA methods are maximum temperature, relative humidity and solar radiation, of which they presented more satisfactory r.

The temperature affects the condition of the vegetation, raising the internal temperature of the plant tissues, dissecting it and contributing to ignition and flammability. The solar radiation directly affects the duration of the preheating period prior to the onset of fire (Machado et al., 2014).

Relative humidity is the predictive factor that contributes most to the burning process. Being a component inversely proportional to the number of foci, it is directly related to the low rainfall, becoming a decisive factor for the occurrence of forest fires, since it affects the vegetation regarding humidity and the availability of oxygen in the plant, favoring the conditions that encourage the combustion process.

The soil temperature variable was not used in the analysis because it presents multicollinearity with the maximum air temperature. The case is the same with the soil water count variable, already taken into account when analyzing the relative humidity of the air that directly influences this variable. The wind velocity variable was not considered either as it is directly related to the propagation of fire rather than to its onset.

The other predictive variables disregarded in the regression model explain the phenomenon in less than 2% because they are indirect terms already associated with the predictive factors.

Table 3 shows a comparison between the data of Table 2 and those found by Torres et al. (2011) on a study of fire occurrence in Juiz de Fora (MG).

Table 3
Comparison of Pearsons correlation coefficient test (r) between the occurrence of fire foci in the Pantanal of Corumbá and in Juiz de Fora (MG) related to the same environmental variables.

Meteorological variable	Correlations (r)
	Corumbá (MS)	Juiz de Fora (MG)
Solar radiation	0.310	0.357
Maximum air temperature	0.383	0.182
Relative humidity	-0.564	-0.467

The correlations of the most significant environmental parameters were close to the meteorological variables analyzed, differing only as to the temperature variable, which is explained by the geographic and climatological differences of the two regions compared.

The monthly variability for the JASON period in the 2005-2015 time series of the number of foci, maximum temperature, relative humidity and solar radiation are shown in Fig. 1, where the profile of the associated burnings can be observed over time, associated with these environmental variables.

Figure 1
Profile of the variability of the monthly averages of meteorological data (Temperature, Radiation and Relative Humidity) and comparison with the total number of foci for the JASON period from 2005 to 2015 in Corumbá-MS.

In general, the highest values of foci correspond to the lowest values of relative humidity, showing the inverse correlation between these two variables, as can be observed for the month of September of 2007 and 2012. The low relative humidity of the air directly influences the vegetation, making it drier, which facilitates the increase of combustible material and consequently the susceptibility to the combustion process. The peaks of foci occurred in August and September of the dry season with an average value of 450 foci.

The mean maximum temperature was 32.3 °C and it can be observed that for the higher temperatures the number of foci is higher, such as August 2005, September 2007, August and September 2012 and November 2014. The temperature showed a significant correlation with the number of foci, but it must be associated with the factor of low relative humidity so that it can be significant within the models, because if the temperature is high and so is the relative humidity of the air, a decrease in the number of foci can be observed, for instance in the months of August 2006 and October 2013.

Solar radiation presented maximum value of 9.2 MJ/m², however a high rate does not mean that the number of foci will be the highest because its incidence is directly affected by the presence of clouds. When low humidity and high temperature occur, the curves are presented in phase, but when analyzed separately, there are lags between the curves of foci and radiation. It can be observed that in September 2007 the curves are in phase and in November 2014 the radiation and temperature are high, however, because of the high relative air humidity the occurrence of foci decreases.

The years 2005 and 2012 should be highlighted for they presented the highest rates of incidence of foci in the series. This is due to the accumulation of fuel material from the plants in the previous years (2004 and 2011, respectively) when high-level floods were reported in the county. The vegetation then turned weaker and propitious to burning when submitted to the climatic conditions of the high temperatures and solar radiation and low relative air humidity in the following years, as can be observed in Fig. 1.

The years 2006, 2011 and 2014 presented a mean number of foci of 170 records, a lower rate resulting from the high relative humidity with the average over 60%.

The Multiple Linear Regression model of fire forecast in Corumbá (MS) is presented in Eq. (3), using the more significant predictor variables of the correlation applied in relation to the number of foci. No multicollinearity was seen between variables, as the tolerance presented values higher than 0.1 and the Variance Inflation Factor (VIF) values were less than 10, as expected.

(3) $$\log \left(\widehat{N}\right)=1.335-0.032R-0.028H+0.050T$$

where $\widehat{N}$ is the estimated value for the number of fire foci; R is the accumulated solar radiation; H is the relative humidity; and T is the maximum daily temperature.

In Table 4 it is possible to observe the descriptive statistics of the applied regression model, with log($\widehat{N}$) as a dependent variable, and the predictors given by variables Solar Radiation, Relative Humidity and Temperature.

Table 4
Descriptive Statistical Analysis of the RLM.

R	Square R	Estimate standard error	Statistics			Durbin-Watson
			Square R change	F change	F change
0.641	0.411	0.64060619	0.411	390.034	0.0001	0.917

The value obtained from R² = 0.411 indicates that the fit degree of the predictive variables was 41%, with p < 0,0001, explaining the output variability , given the meteorological predictors.

The MAPE was 33.9% among the actual values of the base-10 logarithm of the number of foci for the values estimated by Eq. (3), obtained for the same values of environmental variables of the time series analyzed. In applying Stein to the value of R² it can be seen that the result was close to the fit value of 0.410, which means that the model can be generalized for different samples and that the cross-validation of the model occurred.

The statistical analysis resulted in the change of F = 390.034, where new predictor variables inserted in the model by the configuration of IBM-SPSS in stepwise mode were satisfactory for the prediction of foci number, however the hypothesis of independence of errors analyzed by the Durbin-Watson test was partially satisfactory, resulting in 0.917.

Given these analyses, it can be seen that the MLR technique is not the most suitable model for predicting the number of foci, since the model did not seem to be strictly linear. It has yet to be taken into account the possibility of inserting other variables that can contribute to an improved performance of this method, such as a variable associated with anthropic actions.

The results of the comparison of the observed and the MRL-predicted fire foci are represented in Fig. 2.

Figure 2
Comparative graph of the number of fire foci predicted and observed by the MRL model for the JASON period of the historical series from 2005 to 2015 in Corumbá (MS).

According to Fig. 2 it is possible to confirm that the graphs of the observed and the predicted data are in phase with peaks of coincidental maximum and minimum values and tonicities with the same characteristics along the whole curve, in different scales because they have been applied in a parameterized way in the regression using base-10 logarithm.

The residual analysis is plotted in Fig. 3 with the standard distribution residual histogram graphs (Fig. 3a) and the standard regression distribution of the standardized residuals of observed and predicted cumulative probability (Fig. 3b).

Figure 3
Residual graph of the MRL model. (3a) represents the histogram of the frequency-dependent variable vs. the standardized residuals regression. (3b) represents the standardized residual values of the expected vs. observed probability.

Considering the analysis of residuals, it can be observed that the model can be used to make inferences beyond the sample of data used, however it is not the most suitable model for the forecast of the foci because it is not a strictly linear characteristics model and Not to include anthropic action in its predictive variables, which justifies a residual error higher than 60%.

The model is able to explain the variance of the meteorological variables for the prediction of foci as to how propitious they are to occur. In order to improve the prediction of how many foci will occur it is necessary to insert variables that specify the causes of occurrence of each focus (natural or anthropic).

Table 5 shows the result of the application of the Autoregressive Integrated Moving Averages technique – Box-Jenkins’s ARIMA – with four autoregressive terms and ten moving average terms.

Table 5
Descriptive Statistical Analysis of the ARIMA.

Model		Statistics						Ljung-Box Q(18)
	Number predictors	R2	RMSE	MAPE	MAE	BIC normalized		DF	p-value
ARIMA (4, 0, 10)	3	0.665	0.484	31.597	0.381	1.398		11	0.001

onde: RMSE is the root of the mean quadratic error; MAPE is the mean absolute percentage error; MAE is the mean absolute error; BIC is the Bayesian information criterion; DF is the number of degrees of freedom; p-value is the significance.

It was not necessary to differentiate, that is, d = 0, because data were stationary. The number of autoregressive orders was p = 4, requiring four time periods of the series in the past to predict the current value. The value of q = 10 specifies that the deviations of the mean values of the series of each of the last ten time periods are considered when predicting the current values of the series. The analysis of the Bayesian information criterion showed that the ARIMA model (4, 0, 10) is the best predicting model associated with significance p < 0.005. In addition, it is observed that the model fit turns out to be 66.5%, with a mean absolute percentage error (MAPE) of 31.6%, considerably improving the overall performance of the ARIMA model when comparing with the RLM model.

The comparative graph of observed and predicted foci values for the ARIMA forecasting technique is shown in Fig. 4.

Figure 4
Comparative graph of the number of predicted and observed foci by the ARIMA model for the JASON period of the historical series 2005-2015 of Corumbá-MS.

From Fig. 4 it is possible to observe that the curves of the predicted and estimated values are in phase and present the coincidental conditions of tonicity and the peaks of maximum and minimum with the same delineation.

Figure 5 shows the graphs of the residual autocorrelation function (Fig. 5a) and the partial residual autocorrelation function (Fig. 5b) for the ARIMA technique.

Figure 5
Residual graph of the ARIMA analysis, for 24 time intervals of the dependent variables. (5a) Graph represents the residual autocorrelation function (ACF). (5b) Graph stands for the partial residual autocorrelation function (PACF).

The analysis of residuals and the Durbin-Watson test (D = 1.97) showed that the error interdependence hypothesis is satisfied and the overall ARIMA performance was 68.4% with p < 0.002. It is then able to forecast five steps ahead with the same accuracy, as shown in the five categories represented in the graph of Fig. 5, not being necessary the forecast values of the meteorological variables for that same period.

The residual graph analysis revealed that the model is well fitted, since it presents values very close to zero. The estimators are not biased and the ARIMA model presented significantly better results to predict data output of the number of foci.

4. Conclusions

The meteorological factors analyzed establish an important relation with the conditions of vegetation, and directly affect the occurrence of fire points and forest fires, of which the solar radiation, relative air humidity and temperature are enhanced.

It was possible to determine the profile of fire points in the Pantanal biome associated with the meteorological variables and it was observed that the months with the greatest water deficit (JASON period) presented the highest incidence of foci. It is vital to consider that the risk of fire is associated with how propitious the vegetation is under specific meteorological conditions of beginning the combustion process. These estimates, however, do not consider the anthropic factors because of the lack of databases available for this quantification.

Multivariate data analysis techniques were applied by MLR and ARIMA models, where the former explained 41% of variance of the number of foci, thus showing to be a non-efficient technique for prediction.

The modeling of time series using the ARIMA technique (4, 0, 10) presented more satisfactory results, making it possible to explain the variance of the number of foci in 66.5%, which proves to be the most adequate model for forecasting. In order to improve the performance of this technique, the anthropic variable should be inserted, which is a decisive factor for fires to occur, but it is necessary to build such a database so that the performance of new forecast models can be improved.

References

• ARTAXO, P.; OLIVEIRA, P.H.; LARA, L.L.; PAULIQUEVIS, T.M.; RIZZO, L.V.; JUNIOR, C.P. Efeitos climáticos de partículas de aerossóis biogênicos e emitidos em queimadas na Amazônia. Revista Brasileira de Meteorologia, v. 21, n. 3a, p. 168-189, 2006.
• BRASIL. RADAMBRASIL, Ministério das Minas e Energia. Folha SE. 21. Corumbá e Folha SE. 20. Geologia, Pedologia, Geomorfologia, Vegetação e Uso e Ocupação da Terra Rio de Janeiro, 1982, 448 p.
• DEPPE, F.; PAULA, E.V.; MENEGHETTE, C.R.; VOSGERAU, J. Comparação de índice de risco de incêndio florestal com focos de calor no Estado do Paraná. Floresta, v. 34, n. 2, p. 119-126, 2004.
• ESPINOSA, M.M.; PRADO, S.M.; GHELLERE, M. Uso do modelo SARIMA na previsão do número de focos de calor para os meses de junho a outubro no Estado de Mato Grosso. Ciência e Natura, v. 32, n. 2, p. 7-21, 2010.
• FIEDLER, N.C.; MERLO, D.A.; MEDEIROS, M.B. Ocorrência de incêndios florestais no Parque Nacional da Chapada dos Veadeiros, Goiás. Ciência Florestal, v. 16, p. 153-161, 2006.
• GRANEMANN, D.C.; CARNEIRO, G.L. Monitoramento de focos de incêndio e áreas queimadas com utilização de imagens de sensoriamento remoto. Revista de Engenharia e Tecnologia, v.1, n. 1, p. 55-62, 2009.
• HAIR Jr., J.; ANDERSON, R.; TATHAM, R.; BLACK, W. Análise multivariada de dados. 5ª Ed. Porto Alegre: Bookman, 2005, 596 p.
• IBGE. Instituto Brasileiro de Geografia e Estatística Cidades Mato Grosso do Sul – Corumbá MS. Disponível em: http://www.cidades.ibge.gov.br/xtras/perfil.php?lang=&codmun = 500320&search=mato-grosso-do-sul corumba infograficos:-informacoes-completas Acesso em: 08 fev. 2016.
  » http://www.cidades.ibge.gov.br/xtras/perfil.php?lang=&codmun = 500320&search=mato-grosso-do-sul corumba infograficos:-informacoes-completas
• IMASUL. Instituto de Meio Ambiente de Mato Grosso do Sul. Disponível em: http://www.imasul.ms.gov.br. Acesso em: 21 jan. 2016.
  » http://www.imasul.ms.gov.br.
• INMET. Instituto Nacional de Meteorologia. Banco de Dados Meteorológicos para Ensino e Pesquisa. Disponível em: http://www.inmet.gov.br/portal/index.php?r=bdmep/bdmep. Acesso em: 08 fev. 2016.
  » http://www.inmet.gov.br/portal/index.php?r=bdmep/bdmep.
• INPE. Instituto Nacional de Pesquisas Espaciais. Portal do Monitoramento de Queimadas e Incêndios. Disponível em: http://www.inpe.br/queimadas. Acesso em: 08 fev. 2016.
  » http://www.inpe.br/queimadas.
• LEVINE, D.M.; STEPHAN, D.; KREHBIEL, T.C.; BERENSON, M.L. Estatística –Teoria e aplicações usando o Microsoft Excel 3ª ed. Rio de Janeiro/RJ: Ed. LTC, 2005, 819 p.
• LONGO, K.M.; FREITAS, S.R.; SILVA DIAS, M.A.F.; SILVA DIAS, P.L. Emissões de queimadas em ecossistemas da América do Sul. Estudos Avançados, v. 19, n. 53, p. 167-185, 2005.
• MACHADO, N.G.; SILVA, F.C.P.; BIUDES, M.S. Efeitos das condições meteorológicas sobre o risco de incêndio e o número de queimadas urbanas e focos de calor em Cuiabá-MT, Brasil. Ciência e Natura, v. 36, n. 3, p. 459-469, 2014.
• MAGI, B.I.; RABIN, S.; SHEVLIAKOVA, E.; PACALA, S. Separating agricultural and non-agricultural fire seasonality at regional scales. Biogeociences, v. 9, p. 3000-3012, 2012.
• MORETTIN, P.A.; TOLOI, C.M.C. Análise de séries temporais 2ª ed. São Paulo/SP: Ed. Edgard Blüncher, 2006, 531 p.
• NOGUEIRA, J.S.; MUSIS, C.R.; SALLO, F.S.; PRADO, M.J.; PALÁCIOS, R.S. Análise da profundidade ótica de aerossóis e coeficiente de angstrom no cerrado Mato-Grossense. Revista Brasileira de Climatologia, v. 14, n. 1, p. 173-182, 2014.
• NOGUEIRA, J.S.; SANTOS, A.C.A. Análise do material particulado no Pantanal Mato-Grossense. Revista Brasileira de Meteorologia, v. 30, n. 3, p. 254-264, 2015.
• PEREIRA, A.A.; PEREIRA, J.A.A.; MORELLI, F.; BARROS, D.A.; ACERBI JR., F.W.; SCOLFORO, J.R.S. Validação de focos de calor utilizados no monitoramento orbital de queimadas por meio de imagens TM. Cerne, v. 18, p. 335-343, 2012.
• SILVA, R.A. Incêndio Florestal. In: TOCCHETTO, D. Perícia Ambiental Criminal. 1 ed. Campinas: Millennium, 2014. p. 351-406.
• SOARES, R.V.; BATISTA, A.C.; NUNES, J.R.S. Incêndios florestais no Brasil: O estado da arte. 1 ed. Curitiba: Produção Independente, 2009. 246 p.
• SOBRINHO, T.A.; OLIVEIRA, P.T.S.; RODRIGUES, D.B.B.; AYRES, F.M. Delimitação Automática de Bacias Hidrográficas utilizando SRTM. Revista Brasileira de Engenharia Agrícola e Ambiental, v. 30, n. 1, p. 46-57, 2010.
• SORIANO, B.M.A.; PELLEGRIN, L.A. Monitoramento do número de focos de calor e variáveis meteorológicas observados em 2007 no Pantanal. Comunicado Técnico, 64 Corumbá: Embrapa Pantanal, 2007. 3 p.
• TORRES, F.T.P.; RIBEIRO, G.A.; MARTINS, S.V.; LIMA, G.S. Correlações entre os elementos meteorológicos e as ocorrências de incêndios florestais na área urbana de Juiz de Fora, MG. Revista Árvore, v. 35, n. 1, p. 143-150, 2011.
• VIEIRA, H.J.; BACK, A.J.; LOPES F.; MORAIS, H. Estimativa das temperaturas médias diárias, diurnas e noturnas a partir das temperaturas horárias. Revista Brasileira de Meteorologia, v. 27, n. 3, p. 329-336, 2012.

Datas de Publicação

• Publicação nesta coleção
  Apr-Jun 2018

Histórico

• Recebido
  08 Ago 2016
• Aceito
  17 Fev 2018