Balance of photosynthetically active radiation by remote sensing in a seasonally dry tropical forest in Northeastern Brazil

The objective of this work was to characterize the fractionation of Photosynthetically Active Radiation (PAR) and its interaction with the vegetation cover of a portion of Seasonally Dry Tropical Forest at the end of the rainy season in Northeast Brazil. The leaf area index was correlated with each component of the PAR radiation balance to find the best fit models. Second-order polynomial models were used to identify the relationship between the PAR components and the LAI. It was observed that the fractionation of the PAR radiation reflected, absorbed, transmitted, and reflected by the soil and absorbed by the canopy varied according to the class of use and vegetation cover. Besides, as the density of vegetation increased, there was a decrease in the PAR transmitted and reflected, and an increase in the PAR absorbed and, in the PAR, reflected by the soil and absorbed by the canopy, on all the analyzed dates. It was also found that vegetated areas showed greater use of PAR radiation compared to other areas such as urban infrastructure. The vegetation of the São Francisco Valley has great heterogeneity and, consequently, there is a complex relationship with the distribution of photosynthetically active radiation on the surface.


Introduction
Solar radiation with wavelengths between 400 to 700 nm is called Photosynthetically Active Radiation, precisely because of its photosynthetic power, it is essential to plant growth and development, being one of the input variables in ISSN:1984ISSN: -2295 Revista Brasileira de Geografia Física Homepage:https://periodicos.ufpe.br/revistas/rbgfe Fernandes, G. S. T., Lopes, P. M.O., Moura, G. B. A., Silva, M. V. Galvíncio, J. D., Santos, A. models that simulate the accumulation of dry matter during the crop cycle (Liu et al., 2021). Upon reaching a vegetated surface (canopy), this radiation can be absorbed, reflected, and transmitted in different proportions depending on the variation of the sun's zenith angle and factors inherent to vegetation such as phenological stage, size, and leaf architecture (Pereira et al., 2002). Knowledge of the spatial and temporal distribution of PAR in a vegetative canopy is fundamental for understanding the processes of capture and fixation of solar radiation by green biomass, in addition to being an important basis for understanding the local and regional effects of changes in vegetation cover in ecosystem processes (Edreira et al., 2020). This radiation balance is due to the characterization of its components, the fraction reflected by the canopy (RPAR), reflected by the soil (RPARs), absorbed by the canopy (APAR), and transmitted through the canopy (TPAR) (Gallo and Daughtry, 1986).
The determination of this radiative regime in areas of dry tropical forest, represented in the Northeast of Brazil by the Caatinga, is extremely complex, mainly because this biome has high heterogeneity in its phytophysiognomy due to its high diversity of species (Pereira et al., 2021, Machado et al., 2014Silva et al., 2013), which causes a high variation in the density and distribution of vegetation and carbon sequestration Morais et al., (2017).
The dry tropical forest is found in 60% of the Brazilian Northeast and constitutes typical vegetation of the Semi-Arid, which is configured as a hot, dry, and high evapotranspiration region (MDR, 2018). This biome aggregates 5,344 plant species, 318 of which are endemic and, in most cases, are characteristic of tree and shrub forests, with deciduous or xerophytic behavior (Loiola et al., 2012).
One of the limitations in studies involving the radiation balance at the surface is the need for meteorological instrumentation. This methodology encompasses a costly implementation, especially in situations of regional scale. In this sense, the estimation of these components via remote sensing emerges as an effective and economical alternative (Fernandes et al., 2021).
Knowledge of the interaction of vegetation with the PAR provides support for understanding variations in the carbon balance at the surface, characterizing the growth of species, the productivity of an ecosystem, accumulation of biomass, among others (Edreira et al., 2020;Junior et al., 2020;Thun e Mundia, 2020).
Besides, the relevance of carrying out works of this nature is emphasized, because of its scarcity in the literature, especially with the use of remote sensing and in the area under study. Therefore, there are essential contributions in these studies concerning scientific knowledge of the soilplant-atmosphere interaction, the importance of the presence of natural vegetation in the radiative processes of the surface, and in the formulation of environmental and climatic policies aimed at the preservation of the biome.
In this sense, the objective was to characterize the fractionation of photosynthetically active radiation and its interaction with the vegetation cover of a seasonally dry tropical forest at the end of the rainy season in Northeast Brazil. It is assumed that the PAR has different fragmentation in each type of vegetation and that the presence of vegetation contributes to a better use of radiation by the Caatinga ecosystem.

Material and methods
The study area includes the municipalities of Petrolina, located at 9°23'39'' S and 40°30'35'' W, with an average altitude of 380 m; Lagoa Grande located at 8°59'49'' S, 40°16'19'' W and 345 m, both belonging to the state of Pernambuco; Juazeiro which is at 9°24'50'' S and 40°30'10'' W and 368 m and; Curaçá located at 8°59'31'' S, 39°54'28'' W and 366 m. They are located in the Senador Nilo Coelho irrigated perimeter, known as the Vale do Submédio do São Francisco. The land cover in the region is predominantly composed of forest formations of native forests, pastures, and agricultural areas (Figure 1). The Region is part of the northeastern semiarid with a BSwh' climate, according to the Köeppen classification (Alvares et al., 2013), is characterized as hot and dry, with an average precipitation of 571.5 mm.year -1 , an average annual temperature of 26.4 °C, with a minimum average of 20.6 °C, a maximum of 31.7 °C (Lopes et al., 2018) and sunshine of 3,000 hours.year -1 (Ortega and Sobel, 2010).
The predominant natural vegetation is the Hyperxerophilous Caatinga, typical of a hot and dry environment, well adapted to stony soils, with Mimosa tenuiflora (Willd.) Poir., Caesalpinia mycrophylla Mart. ex G. Don (A) and Cnisdosculus phyllancanthus Pax & Hoffm as predominant species and Fabaceae and Euphorbiaceae as more representative families (Calisto Júnior and Drumond, 2014).
The region has smooth-wavy relief ( Figure  2), but containing residual elevations, crystals, and/or peaks that are testimonies of the erosion cycles that occurred in past times in this region (Castro and Santos, 2015). The soils are deep and developed, highlighting Red-Yellow and Yellow Argisols (Silva et al., 2006). Fernandes, G. S. T., Lopes, P. M.O., Moura, G. B. A., Silva, M. V. Galvíncio, J. D., Santos, A. The meteorological radiation data were obtained from the Automatic Meteorological Station (EMA) of the National Institute for Space Research (INPE), located at the geographical coordinates: 09°04'08" S; 40°19'11" W and 387 m, in the municipality Petrolina -PE, in the area belonging to Embrapa Semiárido.
The rainfall data were obtained from the EMA of the National Institute of Meteorology (INMET), located at the coordinates 09°23'18" S; 40°31'23" W and 372.54 m, in the same Municipality. Monthly data were obtained for the months corresponding to the dates of obtaining the images for the years 2009, 2011, 2013, 2016, 2017, and 2019.
The remote sensing data comes from the images obtained from the Landsat 5 TM (Thematic Mapper) sensor, for the years 2009 and 2011, and from the OLI (Operational Land Imager) and TIRS (Thermal Infrared Sensor) sensors, which are onboard Landsat 8, in the years 2013, 2016, 2017 and 2019 (Table 2). Besides, we used the Global Digital Elevation Model Version 3 (ASTER GDEM V003) acquired by the Advanced Spaceborne Thermal Emission and Reflection Radiometer sensor, both with a 30 m spatial resolution (NASA, 2019), used to obtain the slope and transmittance atmospheric.
The Landsat 5,8 (Table 2) and ASTER GDEM V003 images of the region were obtained from the United States Geological Survey (USGS, 2019) for the municipality of Petrolina -PE, which corresponds to the 217/line 66 orbit scene. The Landsat images 5 and 8 were selected considering the absence or little cloud cover (less than 10%) and, because of the purpose of observing the vegetation cover, coming from the end of the region's rainy season, which according to the climatological normal, is set between the months of April to May (INMET, 2019). After clipping the study area, the radiometric calibration of the spectral bands was performed, converting the digital number of each pixel and band into spectral reflectance. The images were cropped and processed using the QGIS 3.6.2 software (QGIS Development Team, 2019).
The procedure started with the calculation of the spectral reflectance. This refers to the solar energy reflected by each pixel per unit area, solid angle, time, and wavelength. To obtain reflectance, it is necessary to convert the quantized and calibrated gray level values of each band, however, using the additive and multiplicative factors related to monochrome reflectance, available in the metadata of the images (USGS, 2019).
Due to the atmospheric interference in solar radiation, mainly due to the absorption and scattering processes, it is essential to correct the planetary albedo, which can be done using the equation of Allen et al. (2002): where, αsup is the corrected surface albedo; αatm consists of the reflectance of the atmosphere itself, with a value of 0.03 being recommended (Bastiaanssen, 2000) and τ sw is the transmissivity of the atmosphere that under clear sky conditions is calculated using Equation 3.
The flux of incident short wave solar radiation or global radiation (Rg, W. m -2 ) was calculated using the following equation (Allen et al., 2002): where, S is the solar constant (1367 W. m -2 ), Z is the zenith angle of the sun, dr is the inverse of the square of the Earth-Sun relative distance and τsw is the atmospheric transmissivity. The radiation portion related to photosynthetically active (PAR, W. m -2 ) was estimated from Rg, using Equation 13 (Tsubo and Walker, 2005).
where, kt is the lightness index (ratio between global radiation and extraterrestrial solar radiation).
The PAR component reflected (PARR, W. m -2 ) by the surface is defined by the reflectance of the vegetation plus that of the soil, considering an area with no water bodies. Thus, this variable was quantified with the following equation: The intercepted photosynthetically active radiation (PARI, W. m -2 ) is characterized as the portion of the incident PAR that is intercepted by the vegetation canopy. This variable was determined through the empirical expression suggested by Daughtry et al. (1992): Fernandes, G. S. T., Lopes, P. M.O., Moura, G. B. A., Silva, M. V. Galvíncio, J. D., Santos, A. Once the PAR and PARI are estimated, the absorbed fraction (PAR A ) can then be determined in W. m -2 using the equation (Souza et al., 2015): Considering that the incident PAR can undergo absorption, reflection, and transmission processes, it is clear that the PAR portion transmitted (PART, W. m -2 ) can be obtained from the following equation (Daughtry et al., 1992): A fraction of the PAR transmitted by the canopy reaches the ground, part of which is reflected by it and absorbed by the lower surface of the canopy. Its determination was made with Equation 18, according to (Daughtry et al., 1992).
where, PARRD is the photosynthetically active radiation reflected by the soil and absorbed by the canopy (W. m -2 ).
The interception efficiency (ε) was estimated as follows: PARi was calculated from the equation: PARi being the photosynthetically intercepted radiation (W. m -2 ), PAR the photosynthetically incident radiation (W. m -2 ) and PARt the radiation photosynthetically transmitted through the canopy (W. m -2 ).
For each year, the ε was related to LAI data to estimate the plant population extinction coefficient. This estimate was made by adjusting the slope of the linear function, based on Beer's law adapted by Monsi and Saeki (1953): PAR component data obtained from the area of native vegetation (area highlighted in purple in Figure 6) were related to the LAI to find spatial distribution patterns and test which is the best fit model. Besides, the determination coefficients (R 2 ), Pearson's correlation coefficients (r) were determined, checking the significance of the coefficients with the t-student test at the 95 or 99% confidence level using Software R version 3.6.1 (R CORE TEAM, 2019). The correlation coefficient was classified according to Devore (2006) according to Table 3.
With the identification of vegetation classes, it was possible to quantify the components of the photosynthetically active radiation balance in each type of class, observing their behavior concerning the variation of plant density. This quantification was performed after disregarding the areas of non-forest formations (pasture, agriculture, water bodies, and urban areas) aiming at their non-interference in the radioactive components (area highlighted in purple in Figure 1) The same methodology was used to identify the distribution of photosynthetic radiation in the classes of land use and cover characterized by the MapBiomas project (MAPBIOMAS, 2019), as shown in Figure 1.

Results and discussion
As it comprises an area of the Caatinga Biome, the vegetation cover of the region has an evident annual variation in the vegetation indices. About the NDVI (Figure 3), it is observed that in 2009, vegetation was predominant with higher NDVI (above 0.391) in areas of natural vegetation and agriculture.
In the years 2011, 2013, and 2017, it is noted that there is a decrease in this index, causing the manifestation of thinner vegetation and the presence of exposed soil areas (yellow color). In 2016 and 2019 it is possible to verify a predominance of denser vegetation, with NDVI ranging from 0.391 to 0.854. It is worth noting that the areas of agricultural production have their NDVI values unchanged concerning time, as these regions are constantly under irrigation, thus preventing the action of environmental factors in their density. The variation in NDVI is mainly related to the variation in total rainfall in the region and, according to Liu et al. (1991), the greatest correlation between these variables occurs when comparing the NDVI with the precipitation of the previous month. Thus, years in which there are more precipitation and greater accumulation of rain in the previous month, such as 2009 and 2019 ( Figure 4), tend to present vegetation with higher values of this index. In contrast, years that obtained lower average NDVI values, such as 2011NDVI values, such as , 2013NDVI values, such as , and 2017, are related to the lower number of precipitations and less rain accumulation in the month before the passage of the satellite (Figure 4). In June 2009, there was a greater number of rainfall compared to the others, one of which was above the climatological average (Figure 9), however, it is noted that the date of the satellite's passage is at the beginning of the month, thus the highest NDVI values are conditioned mainly by the precipitation of the previous month (57.8 mm). In the other years, there was a record of belowaverage rainfall, except for April 2019, which obtained two records above the climatological average of 2 mm. The month of April 2019 is the one with the highest rainfall totals with the accumulation of 7 mm of rain, with the 15th being the rainiest. June 2009 had an accumulation of 5.2 mm, while the other years had accumulations below 3 mm of rain.
The months of May to October constitute the dry period of the region, which justifies the low total rainfall observed in April, on the other hand, it integrates the end of the rainy period that underlies the greatest accumulation of precipitation in that month. According to Silva et al. (2017), in this region, most annual precipitation is concentrated in the first and fourth quarters, with 57 and 24%, respectively. In the second (season evaluated in this study) and third quarters, the percentage is lower, with 16 and 3%, respectively.
Like the NDVI, the Leaf Area Index (LAI) is also related to water availability. Thus, the years 2009 and 2019 showed a higher LAI, as they have more vegetation cover and, consequently, a higher density of vegetation ( Figure 5). In those years, values are predominant between 1.3647 m. m -2 in the areas of forest formation and LAI ranging from 1.3647 to 7.0111 m. m -2 in agricultural areas.  PAR distribution in the São Francisco Valley region follows the same pattern over the years (Figure 7) with values ranging from approximately 311 to 357 W. m -2 . As the slope directly influences the radiation that reaches the surface (Vianello and Alves, 2012) it is observed that in all situations, regions with lower slopes presented lower values of PAR available at the surface, while locations of higher altitudes had higher values of radiation. Studies by Lopes et al. (2013), in the Serra da Mantiqueira, southeastern Brazil, observed that the increase in solar radiation incident with altitude is related to the increase in direct solar radiation and the decrease in diffuse solar radiation. Although the difference in the ranges of variation of the PAR between the images ( Figure  7) is small, this inequality can occur due to solar declination and some factors that act on the transmissivity of the atmosphere at the time of the satellite's passage, such as the presence of cloudiness and the amount of atmospheric humidity, which showed close values between the dates, as can be seen in Table 1.
Days when the solar declination is closer to the latitude of the region cause greater availability of radiation on the surface, thus, images collected in months closer to the day when the Sun reaches the region's vertical location (end of February) have higher values of PAR (image obtained in April, in the fall), showing a decrease as the distance from this event (images obtained in June, in winter).
The PAR data obtained at the meteorological station of the National Institute for Space Research (INPE), are close to those obtained in the satellite estimate, which has an underestimation in the values, as can be seen in Table 5. With the incidence of photosynthetically active radiation, radiative processes begin. These processes are related to the fractionation of the PAR through its interaction with the surface, being predisposed to be reflected, absorbed, and transmitted, which depend on the surface conditions. Vegetated regions tend to absorb and transmit more radiation than regions of exposed soil (Monteiro et al., 2014). It is worth mentioning that factors such as the physiology of the plant species, size, and geometry of the plants; color, size, architecture, and age of the leaves; spatial distribution of vegetation and angle of incidence of sunlight (Pereira et al., 2002) directly affect the PAR fragmentation proportions.
Upon contact with the surface, the first process by which the PAR is submitted is reflection, which is directly related to the albedo. The region of Vale do Submédio São Francisco had the lowest albedos in the years 2009 and 2011 (Figure 9), exposing the prevalence of valuesranging from 0.026 to 0.14 in most of the region, indicating a lower reflectance of solar radiation in these areas. There is a manifestation of areas with an albedo of 0.251, and ranging from 0.363 to 0.475, being related to areas of exposed soil and urban infrastructure. In the other years, the spatial distribution of albedo was similar (Figure 9), with 0.140 to 0.251 as the predominant variation range, where the highest values of this variable are located in areas of thinner vegetation, exposed soil, and urban infrastructure. Areas focused on agriculture, located close to the São Francisco River (Figure 1), showed an albedo of around 0.251 (Figure 9), an albedo characteristic of agricultural areas in this region (Silva et al., 2016;Silva et al., 2019).
Places with higher albedos (0.363 to 0.475) are more expressive and regular in the years 2013, 2016, 2017, and 2019 than in 2009 and 2011, suggesting the existence of more areas with no vegetation. Conti (2011) reports that those areas that show high reflectance due to deforestation, when in large extensions, result in the reduction of available thermal energy, and when aggravated by the absence of cloudiness (favoring the escape of infrared radiation), they can cause a change in the dynamics convective of the region, causing the non-formation of upward convective currents, an unfavorable condition for the formation of rains.
In general, regions of Caatinga (forest and countryside formation) obtained albedo ranging from 0.026 to 0.251, a result that is within the reflectance patterns of natural vegetation in the Caatinga . Areas with this type of coverage have lower albedo values, as the presence of vegetation on the surface alters the dynamics of reflection, since plants, especially large ones, have a high capacity for absorbing solar radiation as a result of reflections multiple inside the canopy (Monteiro et al., 2014).
The areas of water bodies, especially the São Francisco River, showed albedo values ranging from 2.5 to 14% (Figure 9) corroborating these results, Silva et al. (2016) and Silva et al. (2019) found values below 9% of albedo for water bodies in that region.
In this sense, the distribution and density of vegetation directly influence this variable, consequently affecting the quantity of reflected PAR. Figure 10 shows the variation of the average albedo in favor of the vegetation classes (Table 3), it is noted that there is an inversely proportional association between the plant density and the reflectance of the surface, as already reported by Pavão et al. (2015) and Pavão et al. (2017). The reflected fraction of photosynthetically active radiation (PARr) follows the same albedo distribution pattern, as shown in Figure 11, where the highest amounts of PAR were reflected in regions that had lower vegetation densities, exposed soil, and urban areas.
The years 2009 and 2011 obtained in the areas of native vegetation (forest and countryside formation) reflected amounts of 15.03 to 49.01 W. m -2 of radiation ( Figure 11), corresponding to 2.6 and 14% of PAR, respectively. In the other years, these regions exhibited PARr values around 49.01 W. m -2 . Andrade et al. (2014) found the reflected PAR ranging from 0 to 16 W. m -2 , in areas of the Atlantic Forest, values relatively lower than the Caatinga because the Atlantic Forest has denser biomass (Lopes et al., 2013) In agricultural areas, PARr showed a variation from 49.01 to 83.54 W. m -2 (14 to 25.1% of the incident PAR) in the years 2009 and 2011 and a value of 83.54 W. m -2 in 2013, 2016, 2017, and 2019. In urban areas and exposed soil, these values were between 116.33 and 150.75 W. m -2 , representing 36.3 and 47.5%, respectively, of the incident photosynthetically active radiation. The irregularity in the distribution of this fraction of radiation is a direct consequence of the action of the surface reflectance. Therefore, vegetated areas, especially those with large vegetation, tend to have less albedo due to the multiple processes of reflection inside the canopy, as previously emphasized and thus have a lower amount of reflected PAR. Parker et al. (2005) found lower canopy reflectance values in deciduous forest regions in the rainy season, when compared to the same region in the dry season, showing the effect of the presence of leaves on the albedo. Lopes et al. (2013) observed that, in areas of Atlantic Forest, the albedo of the surface varied from 8 to 17% between the rainy and dry seasons.
In contrast, regions, which have the most exposed surface, have a greater capacity for reflection due to the absence of vegetation, so that the "naked" surface, with no component that can trap this radiation, tends to reflect it. Consequences of this type of surface-atmosphere interaction include the reduction of the thermo-hydro regulatory effect of biomass, leading to the priority conversion of the balance of available radiation to the sensitive heat flow, responsible for heating the air Fausto et al., 2016;Pavão et al. 2017).
The amount of PAR absorbed (PARa) by the vegetation varied from 0 to 267.73 W. m -2 , reaching absorption values of up to 74.05% of the incident PAR (Figure 12). The year 2009 presented the highest values of PARa spatially distributed in most of the territory, where there were amounts of radiation absorbed between 133.86 and 267.73 W. m -2 in the areas of forest formation, countryside, pasture, and agriculture.
The other years exhibited a similar spatial distribution, in which the highest values of absorbed radiation were recorded in the agricultural areas, characterizing the fraction of 37.03 to 74.05% (133.86 to 267.73 W. m -2 ) of the Incident PAR. It is noted that agricultural areas have a higher amount of absorbed PAR, this situation is probably due to the higher LAI of these areas when compared to natural vegetation. The efficiency in absorbing the intercepted radiation is directly related to the leaf area index, therefore higher densities of biomass absorb a greater amount of incident radiation.
The fraction transmitted from PAR (PARt) showed a very close distribution pattern between years (Figure 13), in which the largest proportions of PAR (128.78 to 255.23 W. m -2 ) were transmitted in native forest regions, except for 2009, in which these areas had lower values of radiation transmitted through the canopy (0 to 128.78 W. m -2 ), probably due to the higher vegetation rates recorded on this date. The agricultural regions showed to have a smaller amount of transmitted radiation concerning the other vegetated areas (Figure 13), varying from 10.75 to 103.48 W. m -2 , representing from 2.23 to 26.67% of the PAR. Because they have smaller vegetation, the radioactive processes that act in these areas in greater quantity are absorption and reflection, as can be seen in Figures 11 and 12.
The areas that contain vegetation in lower density have a greater amount of radiation transmitted because they have a lesser capacity to intercept radiation, so more voluminous canopies allow less solar radiation to pass through (Andrade et al., 2014). Studying tropical deciduous forests in Mexico, in different seasons (rainy and dry), Parker et al. (2005) showed that in the rainy season the PAR transmittance fraction was lower than in the dry season, precisely due to the greater presence of leaves, since it is a deciduous forest. In an area of the Atlantic Forest, in Alagoas, Andrade et al. (2014) found a variation in the PAR transmitted from 0 to 40 W. m -2 .
Among the PAR subdivisions on the surface, the transmitted portion that is reflected by the soil and absorbed by the lower portion of the plant canopy (PARra) is the one that represents the lowest proportion. It can be seen in Figure 14 that the variation of PARra reaches up to 5% of the incident PAR. The year 2009 stands out for presenting higher values of PARra spatially distributed ( Figure 14) with a variation of 3.75 to 5% of the PAR (12.7 to 16.93 W. m -2 ), possibly because it has a greater quantity of vegetation, the reflective processes that take place inside the vegetation favor the reflection of radiation by the soil and absorption by the abaxial leaf region. The extinction coefficients found ranged from 0.73 to 0.86 (Table 6). These coefficients indicate that the Caatinga vegetation has predominantly horizontally arranged leaves, capable of intercepting a greater amount of photosynthetically active radiation, being more efficient in harnessing this energy. According to Lambers et al. (1998), the extinction coefficient tends to be low for predominantly erect leaves, but it is high for horizontally arranged leaves, especially for larger leaves or leaflets. LAI -Leaf Area Index; ε -Interception efficiency; klight extinction coefficient.
Statistically, clear relationships between the PAR components and the leaf area index can be seen in Figure 15. With little distinction between the dates studied, there are directly proportional relationships between the absorbed fractions (PARa and PARra) and the area index leaf with the  (Table 5), indicating that when there is a higher leaf area index, there is a greater absorption of solar radiation, obviously due to the greater number of leaves exposed to this radiation. The LAI explains the variation of the PAR absorbed by the canopy from 89 to 98%, is significant at the 99% confidence level and probability p < 0.01. Pearson's coefficient (r) ranged from 0.94 to 0.99, indicating a very strong correlation between the two variables. Concerning reflected radiation, although the adjustments found to show the lowest values of R 2 (Table 6), it is noted that there is a triangular formation in the dispersion of the data, indicating a tendency to decrease the reflected radiation as it increases the leaf area index, waiting for behavior according to the data shown in Figure 10. Concerning there was a variation from 0.42 to 0.76, configuring a moderate to strong correlation ( Table  6).
The fraction transmitted from PAR and LAI presented, with an R 2 ranging from 0.90 to 0.98 and r and from 0.95 to 0.99, characterizing a very strong correlation, in which there is greater radiation transmission through the canopy in areas that have a lower leaf area index, since the leaves are attenuating agents of this component through interception and, in their absence, allows PAR to reach the soil more easily, corroborating with Parker et al. (2005), who found higher transmittance values in the dry season, in deciduous forests, which, due to their lack of leaves (absence of LAI), allowed a greater amount of radiation to pass through the canopy. Results also found by Andrade et al. (2014) who describe a reduction in radiation that is transmitted through the canopy as the LAI increases in Atlantic Forest areas in Alagoas.
According to what can be seen in Figure  15, it is noted the importance of the existence of foliage in the fractionation and use of PAR, thus highlighting the relevance of existing vegetation cover, especially in urban areas, because of the benefits of vegetable thermoregulation. In studies carried out in Caatinga by Fernandes et al. (2019), seeking to characterize the energy balance, it was found greater fractions of the radiation balance being directed to sensitive heat in areas of thinner vegetation and of smaller ones in areas of higher density, indicating greater surface heating in less dense areas.
Regarding the balance of photosynthetically active radiation in favor of the different classes of vegetation, it can be seen in Figure 16 that as the density of vegetation increases (class 3 -thin shrubby shrub vegetation to 11 -very dense tree) there is a decrease in PARt and PARr and, an increase in PARa and PARra, on all the dates, analyzed. The data shown in Figure 16 validates the information already mentioned related to how the dense vegetation cover has a greater absorption capacity, less reflection, and less transmission of photosynthetically active radiation. Therefore, there is greater use of this resource when compared to the lower levels of plant density. Besides, it is noted in the distribution of the PAR that the largest proportion, in this type of land cover, is transmitted, corresponding to 50 to 80% of the incident PAR. While the other components vary from 5 to 30% for PARa, from 17 to 20% for PARr, and from 0.4 to 2% for PARra. It is worth mentioning that the distribution of PAR is similar on all the dates analyzed for the coverage of native forests.
More dense areas, such as class 11 (very dense tree vegetation) have the average fractionation of the PAR in 50% transmitted, 30% absorbed, 17% reflected, and 2% reflected by the soil and absorbed by the lower part of the canopy.
In contrast, areas with sparse vegetation, such as class 3 (thin shrubby shrub vegetation) have the average fraction of PAR in 80% transmitted, 8% absorbed, 20% reflected, and 0.5% reflected by the soil and absorbed by the part bottom of the canopy.
The PAR subdivisions in the MapBiomas classification consider the different types of land cover existing in the studied area and can be seen in Figure 1. It is noted that the distribution pattern is similar on the dates evaluated, in which there are different fractions between the classes.
In areas of natural vegetation (3 -Forest Formation, 4 -Savanna, and 12 -Countryside Formation) the largest portions of PAR are destined to the PARt and PARa components, followed by PARr and PARra. In agricultural areas (15 -Pasture, 20 -Sugar cane, 21 -Agriculture and Pasture and 41 -Temporary crops), it is observed that 40 to 50% of PAR is transmitted, applying the same proportion to the portion absorbed, while approximately 20% corresponds to the PARr and PARra components. Areas of permanent cultivation (36) are more similar to the proportions of areas of natural vegetation, due to their size and leaf area. (Figure 17). Figure 17. Average fractionation of Photosynthetically Active Radiation (PAR) in classes of land use and cover, in the Vale do Submédio São Francisco, in the years 2009Francisco, in the years , 2011Francisco, in the years , 2013Francisco, in the years , 2016Francisco, in the years , 2017Francisco, in the years , and 2019 According to Parker et al. (2005) deciduous forests in Mexico, denser than the Caatinga, absorb about 95% of the incident photosynthetically active radiation, of which 50% is absorbed by the leaves, 25% by non-leaf tissues, 20% by the soil, the 5% remaining is reflected by the canopy. In contrast, exclusive areas of natural vegetation in the Vale do Submédio São Francisco (Figure 17), have about 25% of absorbed radiation, 13% reflected, and 62% transmitted.
In general, it is noted that the type of cover directly affects the distribution of photosynthetically active radiation on the surface, which is more used in vegetations that have higher densities. From the data exposed, it is observed that most of the incident PAR is not absorbed by the plants, therefore, it is intended for other purposes such as heating the soil and water, reflected the atmosphere, among others.
According to the data presented, the need for further studies that seek to analyze the radiative processes in native forests is emphasized, mainly aimed at characterizing the impacts of the removal of this vegetation cover and its conversion in areas with other purposes on the availability of energy on the surface and altering biophysical processes once imbalanced in the ecosystem. So that there is the supply of more information to assist environmental planning aiming at the preservation of the biome.

Conclusion
The vegetation in the Vale do Submédio São Francisco region has great heterogeneity, ranging from thin shrub to very dense tree classifications, thus presenting a complex relationship with the balance of photosynthetically active radiation on the surface.
The spatio-temporal analysis of the components of the photosynthetically active radiation balance over the seasonally dry tropical forest showed that most of the incident PAR was destined for transmission (from 50 to 80%), followed by absorption (5 to 30%) and reflection (17 to 20%), varying according to the density of the vegetation.
The relationship between the Leaf Area Index indicates that as the density of vegetation increases, there is a decrease in PARt and PARr and an increase in PARa and PARra. Thus, the dense vegetation cover has a greater absorption capacity, less reflection, and less transmission of photosynthetically active radiation, configuring a greater use of this resource when compared to the lower levels of plant density.