Universidade Federal de Santa Maria

Ci. e Nat., Santa Maria v.42, e105, 2020

DOI:10.5902/2179460X41205

ISSN 2179-460X

Received: 18/11/2019 Accepted: 09/05/2020 Published: 23/11/2020

Meteorologia

Modelling parametrization to estimate atmospheric long wave radiation in the Northern Mato Grosso, Brazil

Carlos Alexandre Santos Querino^I

Marcelo Sacardi Biudes^II

Nadja Gomes Machado^III

Juliane Kayse Albuquerque da Silva Querino^IV

Marcos Antônio Lima Moura^V

Péricles Vale Alves^VI

^I Universidade Federal do Amazonas, Humaitá, AM – Brasil - carlosquerino@ufam.edu.br

^II Universidade Federal de Mato Grosso, Cuiabá, MT – Brasil - marcelo@fisica.ufmt.br

^III Instituto Federal de Mato Grosso - IFMT, Campus Cuiabá Bela Vista, Cuiabá, MT – Brasil - nadja.machado@blv.ifmt.edu.br

^IV Universidade Federal do Amazonas, Humaitá, AM – Brasil - julianekayse@ufam.edu.br

^V Universidade Federal de Alagoas, Maceió, Al – Brasil - malm@ccen.ufal.br

^VI Universidade Federal do Amazonas, Humaitá, AM – Brasil - periclesmat@ufam.edu.br

Abstract

The measures of Atmospheric Long Wave radiation are onerous, which brings the necessity to use alternative methods, such as modelling. Thus, the main aim of this paper was to test and parameterize some models that exist in the literature to estimate atmospheric long wave. The data were collected at Fazenda São Nicolau (2002 - 2003), located in Northwestern of Mato Grosso State. Data were processed hourly, monthly, and seasonal (dry and wet) besides clear and partly cloudy days on the average. The models of Swinbank, Idso & Jackson, Idso, Prata and Duarte et al. were applied. The performance of the models was based on the mean error, square root of mean square error, absolute mean error, Pearson's coefficient and Willmott's coefficient. All models had presented high errors and low Peason’s and Willmott coefficients. After parameterizing, all models reduced their errors and increased Pearson and Willmott’s coefficient. The models of Idso and Swinbank had presented better and worse performance, respectively. It was not observed an increment on the performance of the model when classified according to cloudiness and seasonality. The Idso’s model had presented the lowest errors among the models. The model that had presented worst performance for any tested situation was Swinbank.

Keywords: Statistical Analysis; Meteorological Variables; Long Wave Models

1 Introduction

Atmospheric long wave radiation (LWatm) is linked to the amount of the atmospheric gases and, consequently, to the air temperature. Thus, LWatm is an important variable to the weather and climate studies (AGUILAR et al., 2015). The LWatm is essential to understand the energetic balance and the heating change at the surface-atmosphere interface. Then, to comprehend the modification in its pattern above biomes such as the Amazon forest is crucial to climate studies (AGULAR et al., 2015). The LWatm originates from the atmospheric gases absorption and emission such as Carbon dioxide, Ozone and water vapor, being the last one among the most important (GALVÃO; FISCH, 2000; DAI; FANG, 2014).

The LW plays an important role to the surface thermal condition, because it is one of the unique source of heating that act during the entire diurnal and nocturnal cycle, either from the surface emission (LWsup) or from atmospheric emission (DAI e FANG, 2014). However, despite of all the importance, studies envolving LWatm have been affected due to the uncertaties of the measures because of the poor acurracy or high cost of the equipments with better precision (IZIOMON; MAYER, 2002; DUARTE et al., 2006; SOBRINHO, 2011; AGUILAR et al., 2015). Hence, it is necessary to figure out less onerous alternatives such as estimating the LW by modelling.

Many different models, based on the statistical approach among atmospheric radiation and surface parameters, such as air temperature and water vapor pressure, have been used as an option to reach a better accuracy on the LWatm estimate. The LWatm estimate is a result of the Stefan-Boltmann equation that considers the emissivity (ɛ) and the surface temperature of a certain body. However, the atmosphere temperature and the water vapor pressure are not constants, which brings the necessity to parametrize the models for different meteorological conditions, once almost all of them had been developed to a specific region or climate zone (SWINBANK, 1963; IDSON; JACKSON, 1969;IDSON, 1981; PRATA, 1996; DUARTE et al., 2006).

Thus, parameterize the models to a specific region becomes essential to improve the LW estimate, providing a better quality to the climatic studies. Hence, the main aim of this paper was to test a few models that exist in the literature to estimate LWatm as well as to compare the existent errors before and after the parametrization to determine which one is better applicable to the study region.

2 Material and Methods

2.1. Study Area

The study was carried out in the São Nicolau Farm (SNF) located at the Cotriguacu’s municipality, Northwestern of the Mato Grosso state (09º 47’ 51,32” e 09º 53’ 28,06” S, e 58º 13’ 25,94” e 58º 19’ 37,69” O, between height of 190 and 200 m) (Figure 1). The SNF has an area of around 10 thousand ha in which 2500 ha are pasture areas with reforestation to dioxide carbon fixation (DA SILVA, 2008).

According to Köppen’s classification, the region has a rainy tropical climate “Am”, characterized by two well defined seasonality: wet, among the months of October and April, and dry, throughout the months of May and September (annual amount of rain of 1849 mm). The average temperature oscillate between 23 and 25 ºC and the relative humidity is elevated (IZZO; PETINI-BENELLI, 2011).

Figure 1 – Localization of the Cotriguaçu municipality and the measure tower in the Northwestern of the Mato Grosso state, Brazil

2.2. Meteorological Data

The data of Solar Global Radiation (Rg), Atmospheric Long Wave Radiation (LWatm), Rainfall, Air Temperature (Tair) and Relative Humidity (RH) was collected in a micrometeorological tower (10 m high). The data were collected continuously every 10 seconds and their 30 min average stored in a datalogger CR10 (Cambpell Scientific, UT, USA) (Table 1). The registers were accomplished from May 2002 through April 2003, into a same hydrological year. We highlight that all sensors were previously calibrated before been placed in the field.

As a reference to compare the study year, we used the provisional climate average by using 23 years of data of rainfall, Tair and RH from the municipality of Alta Floresta (09º 52’ S e 56,06’ W, 284m), 300 km far from SNF. The data belong to the Airforce Command Climatological Database.

We reinforce that the criterion to use nearby weather stations was defined according to the World Meteorological Organization (WMO) nº 544, 2003, which determines a horizontal range between weather stations. Generally, this range should not exceed 250 km, or 300 km in lower population density regions, besides having at least 10 years of data to generate the provisional climate average (WMO, 2003).

Table 1 – Description of the equipment used to measure Global Solar Radiation (Rg), Atmospheric Longwave Radiation (LWatm), Rainfall, Air Temperature (Tair) and Relative Humidity (RH), models of the sensors and installation height, at the São Nicolau Farm (SNF) experimental site, Northwestern of the Mato Grosso state, Brazil

Variables	Models	Height (m)
Rg	CNR1, Kipp & Zonen, Delft, Nehterlands	5
LWatm	CNR1, Kipp & Zonen, Delft, Nehterlands	5
Rainfall	TB4 Campbell Sci., Logan, UT, USA	10
Tair/RH	HMP45C, Vaisala Inc., Woburn, MA, USA	8

2.3. Data Processing

The measured data were processed and split in hourly, daily and monthly averages and, afterwards, sorted in wet and dry season, as well as worked for the entire period, here called general data. All tested models had been developed for a non-cloud situation. Thus, to reach the better performance of the models, data were split in clear days (C), but due to the lowest occurrence of clear days, we grouped those data with partially cloudy days (PC). The cloudy classification was carried out based on the atmospheric transmittance index (kt) (Table 2; Equation 1) (IQBAL, 1983).

Table 2 – Cloudy sky condition and range of the atmospheric transmittance index (kt), throughout the study period, for the São Nicolau Farm (SNF) experimental site, Northwestern of the Mato Grosso state, Brazil

Condition	Range
Cloudy	kt < 0,3
Partially Cloudy	0,3 > kt <0,65
Clear	kt > 0,65

 

(1)

where Rg is the solar global radiation and R_o is the solar radiation at the top of the atmosphere (Equation 2). The R_o depends on the latitude (, on the terrestrial orbit eccentricity correction (dr; Equation 3), solar declination (δ; Equation 4) and hourly angle (h; Equation 5).

		(2)
	(3)
	(4)
	(5)

Where dn is the day according to the Julian Calendar.

2.4. Atmosphere Long Wave Radiation Estimate (LWatm)

The estimate of the LWatm is based on the Stefan-Boltzmann law (Equation 6) that consider the air emissivity (ɛ) (DUARTE et al., 2006).

(6)

Where σ = 5,67051 x 10^-8 W m^-2 K^-4 is Stefan-Boltzmann’s constant and  is the absolute air temperature.

Five models have been tested in this study, which are applicable to the temperature range (Table 3). The first two models have been proposed by Swinbank (1963) and Idso and Jackson (1969) and consider, in their estimate, only the Tair. The other models have been proposed by Idso (1981), Prata (1996) and Duarte et al. (2006) and consider, in their estimation, besides Tair, the water vapor pressure (ea) in hPa (Equation 7) (IDSO, 1981; PRATA, 1996; DUARTE et al., 2006).

(7)

Where e_s is the saturation pressure of the atmospheric water vapor determined by Teten’s equation (Equation 8) (TETENS, 1930). In the Prata’s model, the e_a is determined by the ξ determined by Equation (9).

	(8)
	(9)

Table 3 – Methods and respective original models proposed to estimate the atmospheric emissivity for the São Nicolau Farm (SNF) experimental site, Northwestern of the Mato Grosso state, Brazil

Method	Original Models	Range of Temperature (º C)
SWINBANK (1963)		2 to 29
IDSO and JACKSON (1969)		- 29 to 37
IDSO (1981)		- 40 to 45
PRATA (1996)		- 40 to 45
DUARTE et al. (2006)		- 40 to 45

2.5. Statistical Analysis

The hourly, daily and monthly averages with ± 95% confidence interval for the LWatm estimate, before and after parametrization, have been calculated through by bootstrapping the resampled time series over 1000 iterations by using the Package Boot to R software (EFRON and TIBSHIRANI, 1994).The performance of the models to estimate the LWatm was evaluated by the calculus of the Mean Absolute Error (MAE; Equation 10), Root Mean Square Error (RMSE) (Equation 11) and Percentage Mean Relative Error (PMRE) (Equation 12).

	(10)
	(11)
	(12)

Where P_i are estimated values, O_i are measured values and n the total amount of samples.

The performance of the models was also checked by two coefficients: i) Willmott’s coefficient d (Equation 13) which indicates the concordance level of the estimate when compared to the measured values (WILLMOTT et al. 1985). The value of d must oscillate between 0 and 1 indicating non-concordance or perfect match, respectively (MACHADO et al., 2015); and ii) by the Pearson’s coefficient (r) that indicates the level of correlation among the estimated and measured values and also indicate non-match (r = 0) and strong match (r = 1) among the data.

(13)

3 Results and Discussion

3.1. Meteorological Variables

The amount of rainfall to the study period (2244 mm) was of 394.6 mm above the historical average (1849.40 mm) (Figure 2a). However, this anomalous value of rainfall has occurred due to the excess of rain throughout the wet season, which had registered 381 mm over that expected (1684 mm expected and 2065 mm registered). From the total amount of rainfall for the wet season 573 mm had occurred during March. This anomaly of rainfall is related to two factors that are directly linked: i) the influence of El Niño phenomenon that was classified to the study year as moderate category (CLIMANÁLISE, 2003). The acting of the El Niño modifies the pattern of the atmospheric circulation and causes intense rainfall in some regions and drought and others (MARENGO, NOBRE, 2009); ii) in this specific case, throughout the period of 10 to 12 and 19 to 21 of March, it was observed that the Bolivian High (BH) pressure system was acting displaced to the center of Brazil and placed over Mato Grosso as a consequence of the El Niño (CLIMANÁLISE, 2003). Thus, the BH contributed to increase the rainfalls in this region that registered, in this six days, almost 40% of the total amount expected for March. The BH is one of the main system that causes rainfall in the Brazilian center-western region and is defined as a strong anticyclone located in high levels of the atmosphere mainly formed by the surface convective heating (ALVES, 2009). During the dry season, which is caused by the inhibition of the BH acting, the total of rainfall, the total amount of rainfall to the study period (178 mm) was according to the climate average (164 mm).

Figure 2 – a) Measured rainfall and provisional climate average (CA), b) Solar Global Radiation (Rg), c) Long Wave (LW), d) Net Radiation, e) Measured Air Temperature and provisional Climate Average (Tair) and f) Measured Air Relative Humidity (RH) and provisional Climate Average, for São Nicolau (SNF) experimental site, Mato Grosso, Brazil, throughout May 2002 to April 2003

 

The Rg has presented the annuals and dry and wet seasons averages of 203, 207 and 203 W m^-2, respectively. the highest averages had been registered in the months of June (220 W m^-2), October (223 W m^-2) and November (219 W m^-2) (Figure 2b). June stands out to be the winter solstices for the Southern Hemisphere and should present less Rg. However, in the study year, June and July were extremely dry, with lower or none rainfall registered and, consequently, lower cloud cover, increasing the incoming solar radiation Rg. The months of October is considered the begin of the wet season, but, in 2002, it was registered rainfall lower than the climate average, which contributed to reduce the cloud cover besides the fact of this month be the one in which the Sun zenithally culminates above the region. The zenith culmination of the Sun implies downright rays incidence, due to the lower zenith angle and, consequently, shorter optical way at the atmosphere. Hence, the light beam reach more directly on the surface and less radiation is spread in the atmosphere (QUERINO et al., 2006).

The monthly Tair averages were below the CA, but with similar pattern (Figure 2e). The highest average was registered at the end of the dry season (~26 ^oC for August) and lower in June (~24 ^oC). Among the seasons, it was observed that there was no variation on the average temperature (~25 ^oC). These results to the Tair are reflected in the RH, once these variables have inverted pattern. In this way, the season with the lowest averages of RH (dry season ~77%) are associated to the highest Tair values, whereas during the wet season it was registered the biggest averages of RH ~ 84% and lowest Tair.

The RH was during the entire study period (~ 81%) above the CA. The fact of the Tair and RH being respectively lowest and highest than the historical data, is related to the microclimatic conditions of the region. Specifically for these two variables, small changes in the environment cause variations on the measured values. The measure station in the SNF is installed in a region surrounded by forest, while the climate historical data have been registered by the weather station of Alta Floresta airport in an urban zone. The insertions of the weather stations in urban area have registered those microclimate effects and trends, such as register of higher air temperature due to the addition of the heating originated by the atrophic actions (TEODODO; AMORIM, 2008). The increment on the Tair and reduction on the RH happen mainly due to the change on the soil heating partition, because most part of the incoming energy is used as sensible heating source (BIUDES et al., 2015).

The annual dry and wet season average of the LWatm was 414, 496 and 422 W m^-2, respectively. The lowest record was registered in June (391 W m^-2) and, the highest average happened in January (427 W m^-2). the surface component (LWsur) registered the annual average of 448 W m^-2, while both dry and wet seasons registered similar averages (449 W m^-2).

The oscillation of the LWatm throughout the year happen due to the seasonality effects of the region. The months considered dried show low RH indices (Figure 2f) besides low rainfall records, lower cloudy concentration and, as consequence, less emission of LWatm, once the water vapor is one of the most important gases to absorb and emit LWatm (RÄDEL et al., 2015). This relation is highlighted when we observe the Pearson’s correlation index (r) and the significance level p Value among LWatm and Tair, RH and e_a variables. In the SNF, it was observed strong correlation and high significance level when related LWatm with RH and e_a (Table 4). On the other hand, the small oscillation of the LWsur is related to the kind of the soil cover that will influence the surface temperature.

The region where the SNF tower is installed is a pasture area surrounded by flooded forest. To the study year, it was not observed high variation in the averaged surfaced albedo among dry (0.20) and wet (0.19) seasons. Thus, it is expected that the amount of incoming solar radiation that is stored in the system do not vary throughout the year, providing the same amount of energy to be changed in thermal radiation and emitted to the atmosphere (IZIOMON; MAYER, 2002).

The net radiation (Rn) has shown annual average of 134 W m^-2 in the wet season and 128 W m^-2 in the dry season (Figure 2d). The standard pattern of Rn was similar to Rg. The short wave balance tends to be controlled by the surface albedo, as mentioned before. The albedo to the analyzed year had not varied among the seasons, then, the Rn was driven by the Rg probably because it is the mainly source of energy on the surface – atmosphere system (DAI; FANG, 2014; QUERINO et al., 2017).

Table 4 – Pearson’s correlation coefficient (r) 95% of significance of the monthly averages in the experimental site of SNF, Cotriguaçu, Mato Grosso, Brazil

	Tair	ea
LWatm	0,213812	0,956174
p-value	0,504603	0,000001

3.2. Atmospheric Longwave Radiation Estimate (LWatm)

The models of Swinbank (1963), Idso and Jackson (1969), Idso (1981), Prata (1996) and Duarte et al (2006), when compared before and after the parametrization, had shown improvement when tested the general data, whereas, without classifying data by cloudiness or seasons (Table 5 and 6). Idso and Jackson (1996) and Idso (1981) models had shown MAE equals to zero. Although Idso’s (1981) model stands out among the others because it does not show high difference among the errors and the values of r and d before and after parametrization. Swinbank’s model was considered to be among the worst models after the parametrization considering the general data because it had presented the worst MAE, RMSE and PME and the lowest r.

Under the condition of partially cloudy sky throughout the year without distinction among dry and wet seasons, the study had shown significant improvement on the errors for all models, with a suitable upgrading in the d, but with not big difference to r (Tables 5 and 6). When comparing the parameterized table with general data to general data classified by cloudiness (Table 6), it is noticed that both errors, d and r did not show modification.

All the models had presented improvement in the error, d and r values during the wet season (Tables 5 and 6). Nevertheless, when compared values from Table 5, it was observed that all the errors either were kept constant or had presented a smooth improvement. On the other hand, the values of d and r had shown to be worst in their results. During the dry season, was observed, in general, that the condition of CL and PC had presented the worst errors. The d and r, in spite of showing a little improvement, when compared to the wet season, was kept almost constant, when compared to the data of CL and PC sky conditions without being classified by dry or wet season (Tables 5 and 6).

Among all the tested models, the one that had shown the worst performance related to the r and d, for all situations, were Swinbank and Idso and Jackson models. The lowest performance of these models can be attributed to the fact that they assume that the air moisture is an implicit function of the Tair and, consequently, that does not express explicitly the water vapor in their formulations (IZIOMON et al., 2003). As the other models consider the e_a (water vapor pressure), we can justify their better performance because the water vapor is considered one of the main emitters of LWatm (RÄDEL et al., 2015).

Table 5 – Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Percentage Mean Relative Error (PMRE), and their respective Willmott’s d and Pearson’s r estimate coefficient for the models of Swinbank (1963), Idso and Jackson (1969), Idso (1981), Prata (1996) and Duarte et al (2006), simulated for different conditions, before the parametrization, for the experimental site of São Nicolau Farm – SNF, Mato Grosso, Brazil

Conditions	Models	MAE (W m-2)	RMSE (W m-2)	PRME (%)	d	r
General Data	Swinbank	34.6	42.9	8.93	0.51	0.51
	Idso e Jackson	31.4	40.8	8.43	0.54	0.51
	Idso	7.1	17.1	3.40	0.82	0.71
	Prata	17.7	26.4	5.22	0.65	0.57
	Duarte	39.1	42.6	9.43	0.51	0.65
General Data and Clear /Partially Cloudy Days	Swinbank	33.2	41.7	8.65	0.53	0.53
	Idso e Jackson	30.0	39.7	8.16	0.56	0.53
	Idso	7.7	17.3	3.44	0.82	0.73
	Prata	18.8	27.1	5.39	0.65	0.59
	Duarte	38.2	41.7	9.23	0.52	0.67
Wet period and Clear /Partially Cloudy Days	Swinbank	40.6	46.0	9.79	0.42	0.54
	Idso e Jackson	37.3	43.5	9.12	0.44	0.54
	Idso	5.4	15.9	3.01	0.75	0.59
	Prata	12.3	20.9	4.01	0.67	0.56
	Duarte	43.1	45.7	10.24	0.41	0.59
Dry period and Clear /Partially Cloudy Days	Swinbank	23.5	35.4	7.16	0.62	0.59
	Idso e Jackson	20.4	34.1	6.91	0.64	0.59
	Idso	10.6	18.9	3.99	0.80	0.73
	Prata	27.3	33.5	7.20	0.60	0.64
	Duarte	31.7	35.7	7.91	0.57	0.70

 

Table 6 – Parameterized Equation, Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Percentage Mean Relative Error (PMRE), and their respective Willmott’s d and Pearson’s r estimate coefficient for the models of Swinbank (1963), Idso and Jackson (1969), Idso (1981), Prata (1996) and Duarte et al (2006), simulated for different conditions, after the parametrization, for the experimental site of São Nicolau Farm – SNF, Mato Grosso Brazil

Conditions	Models	Equations	MAE (W.m-2)	RMSE (W.m-2)	PRME (%)	d	r
General Data	Swinbank		3.3	27.2	5.65	0.69	0.51
	Idso andJackson		0.0	17.9	3.65	0.64	0.52
	Idso		0.0	14.5	2.96	0.81	0.72
	Prata		0.4	17.1	3.57	0.83	0.69
	Duarte		0.4	17.3	3.61	0.82	0.69
General Data and Clear /Partially Cloudy Days	Swinbank		1.5	27.1	5.62	0.70	0.53
	Idso&Jackson		0.0	17.9	3.66	0.67	0.54
	Idso		0.0	14.5	2.96	0.82	0.73
	Prata		0.4	17.0	3.55	0.84	0.71
	Duarte		0.4	17.1	3.59	0.83	0.70
Wet period and Clear /Partially Cloudy Days	Swinbank		1.3	23.7	4.81	0.68	0.54
	Idso&Jackson		0.1	14.1	2.78	0.68	0.54
	Idso		0.0	13.1	2.59	0.72	0.61
	Prata		0.4	16.2	3.27	0.77	0.60
	Duarte		0.4	16.2	3.29	0.77	0.59
Dry period and Clear /Partially Cloudy Days	Swinbank		1.9	28.0	5.91	0.72	0.59
	Idso&Jackson		0.1	17.0	3.62	0.72	0.59
	Idso		0.0	13.9	2.97	0.83	0.75
	Prata		3.2	17.6	3.85	0.84	0.73
	Duarte		0.5	17.1	3.71	0.84	0.71

 

The models presented the worst performances in the afternoon and after midnight, when compared the LWatm measured and estimated by the models, when observed general data (Figure 3a). The same situation was also observed after classifying the data in Clear (C) and Partially Cloudy from the general data (Figure 3b) for the wet season (Figure 3c). We underscore that the Figures (3a, 3b and 3c) show that the models proposed by Prata (1996) and Duarte et al. (2006) had presented a similar pattern and their lines overlapped in all time of the day, but underestimate the measured value before the dawn and overestimate it throughout the afternoon. Idso and Jackson (1969) and Idso (1981) models had also shown the same trend to overestimate during the afternoon and underestimate before the dawn, but with less difference between the estimated values.

Figure 3 – Averaged day of the Atmospheric Longwave Radiation (LWatm) measured and estimated by the 5 models, classified according to the data: a) General, b) Clear and Partially Cloudy days to the general data, c) Clear and Partially Cloudy days to the dry season and d) Clear and Partially Cloudy days to the wet season to the São Nicolau Farm – SNF, Mato Grosso, Brazil

 

The models had a pattern near to the measured values just during the early morning during the dry season (Figure 3d). Throughout this season, was observed an increment of the errors (Table 6), which reflected a biggest discrepancy between measured and estimated values. The increment of the errors in the dry season increases the difference between Prata (1996) and Duarte et al. (2006) models, the same one that overlapped on the 3 previous situations. The Swinbank (1963) model had presented the worst performance among all the models tested in all the analysis situation. The variation of the Idso and Jackson (1969) and Idso (1981) models, for all situations, was null and only took place from the second decimal place.

5 Conclusions

It was not observed an increment on the performance of the model when classified according to cloudiness and seasonality. Hence, all the models here presented can be applied without the necessity of classification according to the cloud condition, because all the models had presented a smoothly decreasing on their performance when classified by cloudiness and season.

The Idso’s model had presented the lowest errors before the parametrization, when compared to the other models, and little difference among the errors after parametrization, which indicate that it can be applied even without parametrization. Among all the models, the one that presented the worst performances for any tested situation was Swinbank (1963).

Acknowledgment

The current research was partially funded by the Universidade Federal de Mato Grosso (UFMT), Instituto Federal de Mato Grosso (IFMT), Programa de Pós Graduação em Física Ambiental (PPGFA) IF/UFMT, Coordenação de Aperfeiçoamento de Pessoal do Ensino Superior (CAPES) under Grants 9750/13-4 and 9768/13-0, Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) under Grant 303625/2015-5; 310879/2017-5; Edital Universal/CNPq - 407463/2016-0], Fundação de Amparo à Pesquisa do Estado de Mato Grosso, under Grant [PRONEX/FAPEMAT - 823971/2009; Edital Universal/FAPEMAT - 331763/2012; FAPEMAT – PRONEM - 561397/2014].

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