Analysis of Measurements of Direct Normal and Global Solar Radiation for Maceió, Alagoas State, Northeastern Brazil

Abstract Studying solar radiation is essential for human knowledge, since it is present in practically all its activities. Thus, the aim of this work was to analyze the climatic and seasonal variation of direct normal and global solar radiation in the region of Maceió, Alagoas State, Northeastern Brazil with sky conditions characterized by clearness index (Kt). The Kt was determined by the ratio between global solar irradiance and solar irradiance at the top of the atmosphere. The highest occurrences of daily direct normal solar irradiance under conditions of Kt ≥ 0.6 were recorded between 400 W m−2 and 700 W m−2 for all seasons. Under conditions of 0.4 ≤ Kt < 0.6, the daily direct normal solar irradiance occurred between 200 W m−2 and 500 W m−2 and for conditions of Kt < 0.4, its maximum value was 200 W m−2. It was observed that the levels of solar incidence in the study region depend on cloud cover conditions, with little influence of seasonality.


Introduction
The radiation emitted by the Sun that arrives at Earth (top of the atmosphere and terrestrial surface) is the main source of energy that influences practically all human activities (Liou, 2002;Muneer, 2004;Santos et al., 2014). The knowledge of the global solar irradiance (I G ) which is measured on a horizontal surface, direct normal solar irradiance (I D ) and diffuse solar irradiance (I d ) has great importance in several scientific and technological areas, e.g. meteorology, climatology, energy generation, agrometeorology, and others (Vick et al., 2012;Tabari and Talaee, 2014;Evseev and Kudish, 2015;Ferreira Junior et al., 2015;Santos et al., 2016).
Thus, solar radiation studies require reliable and readily available data series for applications at the site of interest. The instrumentation to obtain I G and I D time series is given by the installation of a network of solar monitoring stations with radiometers and data acquisition system. The amount and spectral distribution of I G and I D depend on astronomical, atmospheric and local parameters such as: solar zenith angle, aerosol concentration and properties, amount of ozone, clouds, altitude of the site and surface albedo (Kaskaoutis and Kambezidis, 2009). I D is very sensitive to the optical depth of the aerosol and exhibits high frequency variation to the dynamic effects of clouds, showing greater spatial and temporal variability than I G , making it difficult to characterize daily and seasonal variability of solar radiation and its components (Kotti et al., 2014).
The climatic characterization of the solar radiation requires a series of long-term measurements. However, the availability of solar databases, especially long time and continuous I D is scarce. With the availability of measurements, different researchers studied the climatic characteristics of solar irradiance, especially the work of Liu and Jordan (1960). In Beer Sheva -Israel, Evseev and Kudish (2015) analyzed solar irradiance from 1985 to 2013 and observed that the site has high frequency of clear sky days. In Seville -Spain, Moreno-Tejera et al. (2016) showed an analysis of solar irradiance variation, applying a statistical characterization in different time partitions.
Despite the importance and interest of the scientific and governmental community, the knowledge of solar irradiance components on the surface is still in its beginning in the Brazilian territory, mainly because it is a country of great territorial extent. In Brazil, there are few solarimetric stations that simultaneously perform high quality measurements of I G and I D components. Studies analyzing databases of solar components are not so often found in specialized literature; however global solar radiation for several sites in Northeastern Brazil (NEB) has been evaluated (Tiba, 2001). The seasonal variations of the diurnal evolution of solar irradiance components based on measurements collected on the surface of the city of São Paulo -Brazil (Oliveira et al., 2002). The global solar irradiation was evaluated in Maceió (NEB) (Souza et al., 2005), showing a lower monthly average daily value in July and higher in November, with dry season (October-February) average hourly values 12.26% higher than values in the rainy season (April-August). Analyzes and comparisons of solar components were made for the city of São Paulo and rural area of Botucatu-SP (Codato et al., 2008), in which, although located in similar latitude and altitude, the seasonal evolution of the daily values indi-cates that São Paulo receives, during the days of open sky, 7.8% less in August and 5.1% less in June than Botucatu. An observational characterization of the diurnal and seasonal variation of the solar irradiance components for Rio de Janeiro has been Marques Filho et al. (2016).
The research site is located in the metropolitan region of Maceió, with sugarcane cultivation in the vicinity, bathed by the Atlantic Ocean and large lagoons; thus, the local atmosphere is polluted by particulates originating from industries, burning and local fires, and elevation of the water vapor concentration that attenuates I G and, mainly, I D . These very small solid or liquid particles, called aerosols, are determinants of the spread of I D . On the other hand, water vapor acts in the earth's atmosphere as an I D absorber. The combined action of aerosol concentration and water vapor content significantly affects the magnitude and variability of I D , influencing the transparency level of the atmosphere. The importance of solar radiation characterization for the region where there is a growing demand for solarimetric information for solar energy, fundamental for establishing public policies in the area of renewable energy is also highlighted. Thus, this paper presents a climatic and seasonal analysis of the effects of sky cover on I G and I D values in the metropolitan region of Maceió between years of 2011 and 2014.

Study area
The measurements used in this study were obtained from the solarimetric station located at the Federal University of Alagoas (9°33' S; 35°46' W and 100 m a.s.l.), in Maceió, capital of the State of Alagoas, located in eastern NEB (Fig. 1). The microregion of Maceió is located on the coast, with variation of altitude between (0 and 20) m in the lower region (coastal plain), between (20 and 180) m on the slopes and coastal boards, reaching 300 m at the northern end of the municipality (Fig. 1). This variation can cause changes in air temperature and winds. The solarimetric station is installed at 15 km from the Atlantic Ocean, with herbaceous vegetation and Atlantic Rainforest and hot and humid climate.
Alagoas is subdivided into three geographic mesoregions (Coastal/Humid Zones, Hinterland and Interior) with different types of climate and further details are described in Santos et al. (2014), Santos et al. (2016) and Barros et al. (2012). The microregion of Maceió is part of mesoregions of Coastal/Humid Zones. This mesoregion have hot and humid climate, with annual rainfall varying from 600 to 3000 mm, the rainy season is concentrated between autumn and winter (from May to August), with 55.2% of the annual rainfall and the dry period occurs between spring and summer (November to February) with only 12.5% of the total rainfall (Lima, 1991;Souza and Lima, 1995;Molion and Bernardo, 2002). The rainfall regime of the State of Alagoas is associated with several meteorological systems common to much NEB. Among the main systems, the coastal instability lines, seasonal variation of trade winds, position and intensity of the Intertropical Convergence Zone (ITCZ), Upper-Level Cyclonic Vortexes (ULCV), Eastern Waves (EW), are highlighted as the main ones (Souza et al., 2004;Lyra et al., 2014). In general, Alagoas has rainy season between May and July, when there is the maximum convergence of trade winds with the terrestrial breeze, which should be stronger during the autumn and winter seasons when the temperature contrast between land and sea is higher (Kousky, 1980), and a dry season between November and January, a period in which a shift in the direction of trade winds takes place, which impairs the formation of clouds in the region.

Obtaining data
In this study measurements of global solar irradiance (I G ) and direct normal solar irradiance (I D ) were obtained from 2011 to 2014. Due to technical/operational problems, the I D database used is not continuous over the measurement period. The lack of electricity and non-linearization of the sensor with the solar disk are some factors responsible for significantly reducing the database. The  component was measured by sNIP model secondary standard pyrheliometer assembled on an automatic solar tracker (Fig. 2) manufactured by Eppley. All sensors used followed the maintenance and calibration procedure according to manufacturer's recommendations (periodic calibration). Periodic checks throughout the measurements were made to ensure that the radiometer domes were clean, obtaining accurate and reliable measurements.
The radiometers used were connected to a Micrologger 21XL (Campbell Scientific Inc), with frequency of 1 Hz and programmed to take readings every 10 s and store the average every 10 min. Hourly and daily data are calculated from the average values of 10 min. The collected I G and I D data were integrated to produce global solar irradiation (H G ) and direct normal solar irradiation (H D ) on hourly (H G h and H D h ) and daily (H G d and H D d ) basis, respectively. A quality control process is essential before using any database of the place of interest. The quality of individual measures was verified according to recommendations of the World Meteorological Organization (WMO, 2008).

Statistical and climatic analysis of measurements
The measures of I G (H G ) and I D (H D ) in the hourly and daily time partitions were analyzed considering seasonality and local cloud cover. For statistical and climatic analysis of measurements, solar irradiance components were separated into periods and characterized in the different seasons of the year according to the region climatology, which is strongly dependent on the seasonality of precipitation and air temperature (Souza et al., 2004). In the Maceió region, the rainy season begins in April and ends in August, while the dry season begins in October and extends through February. Based on this seasonality and for further study, the climatic periods were separated into four: 1 -the dry (less rainy) period was separated into Dry Season (DS) (November to February); 2 -the transition period between dry and rainy season (March and April) was separated and defined as Pre-Rainy Season (PRS); 3 -the rainy season (May to August), will be called here as the Rainy Season (RS); 4 -the transition period between the rainy and dry season (September and October) was denominated as Pre-Dry Season (PDS).
The cloud cover was characterized from clearness index (K t ) values in the hourly (K t h ) and daily (K t d ) partitions, determined by the K t = I G /I 0 ratio. Thus, based on Iqbal (1983), some adaptations were made regarding K t intervals to the atmosphere of Maceió, when (K t ≥ 0.60), the conditions are of Clear Sky (CS); when (0.40 ≤ K t < 0.60) characterizes Partially Cloudy Sky (PCS) condition and for (K t < 0.40) it characterizes Overcast Sky (OS). For the representation of irradiance curves (irradiations) and estimates, days representing the different cloud cover conditions in each of the stations were randomly chosen. The I G and I D variations were elaborated with average mea-sures of 10 min, and hourly curves of H G h and H D h were plotted from the integration of the irradiance curves for each hour. Irradiance and irradiation analyses were performed between the interval between 06:00 am and 05:00 pm, comprising practically the entire daytime period of solar incidence.
The average value of solar irradiance (global and direct) were separated into three different cloud cover conditions and four-time intervals. The average hourly of global solar irradiance (I

Calculation of solar irradiance at the top of the atmosphere
The solar irradiance at the top of the atmosphere (I 0 ) was calculated by Eq. (1): in which I SC is the solar constant (1367 W m −2 ), E 0 is the correction factor of the eccentricity of the, further details are described in Souza et al. (2005) and Iqbal (1983). I 0 data were integrated to obtain the solar irradiation values at the top of the atmosphere (H 0 ), hourly (H 0 h ) and daily (H 0 d ).

Climate and Weather system
The climate of Maceió is "As" type, characterized as rainy tropical, with rain in the winter and autumn and dry in the summer (Köppen classification). The air temperature is high (> 20.0°C), with monthly thermal amplitude equal to 2.9°C, average air temperature of 23.9°C in the coldest month (July) and 26.6°C in the hottest (March), the average is 25.4°C (Fig. 3a). In spring and summer, it is common to have days with maximum air temperature above 30.0°C, whereas in autumn and winter, daily air temperatures rarely reduce values below 20.0°C. The relative air humidity presents low annual fluctuation, with monthly average values greater than 75% (Fig. 3a), which is due to its proximity to the Atlantic Ocean. Rainfall in the wettest month is 341.9 mm (June) and in the least rainy month 30.2 mm (December); summer precipitation is approximately 293.4 mm (Fig. 3b). Spring is the season with the lowest precipitation (168.8 mm).
From November to March, precipitation is usually attributed to the convergence between the land breeze and the southeastern trade winds; however, in this time of year, this does not occur often, since a shift in the direction of trade winds decreases the intensity of the encounter with the terrestrial breeze, with lower contrast between the surface and the ocean temperatures. Another meteorological phenomenon contributing to the precipitation during this time of year is the ULCV, characterized as closed cyclone circulation with subsiding air in the center, and in these systems, the center has Clear Sky; however, its peripheries are submitted to large amounts of precipitation (Molion and Bernardo, 2002;Reboita et al., 2012). The precipitation reaches 820.2 mm and 527.2 mm in the autumn and winter, respectively. In the rainy season (April to August) precipitation is caused due to the action of some weather systems dependent on the effect of some surface and atmosphere configurations. We can highlight the occurrence of the penetration of frontal systems that may in some cases reach equatorial latitudes (Kousky, 1979), the convergence of trade winds with the terrestrial breeze that reaches its peak during the autumn and winter seasons with the increasing contrast of temperature between earth and ocean (Kousky, 1980), the eastern undulating disturbances known as eastern waves (EW) (Chou, 1990;Espinoza, 1996), and finally the action of the South Atlantic Convergence Zone (SACZ) when moved to lower latitudes (near Equator). The SACZ configuration is related to the ITCZ positioning, causing good part of the precipitation in Maceió (Molion and Bernardo, 2000). The month of December has the longest sunshine duration (SD) (260.4 hours), followed by November (259.2 hours) (Fig. 3b). The months of June (164.7 hours) and July (165.4 hours) are those with the lowest SD.
In addition to its proximity to the Atlantic Ocean, Maceió is also influenced by the presence of two large lagoons: Mundaú and Manguaba. The Mundaú lagoon has an approximate reservoir of 23 km 2 and Manguaba with 42 km 2 . Both are located within a radius of 15 km south of Maceió. Their dimensions represent a local microclimate, causing interference in the atmosphere and in the microphysics of clouds. With the convection of the ocean and lagoons, the region of Maceió is strongly influenced by water vapor for most of the year (Fig. 4), helping in the formation and predominance of cumulus clouds in the local atmosphere. Water vapor accompanies the annual trend of air temperature and SD, increasing values in spring -summer and decreasing in autumn -winter.

Analysis of solar irradiance under clear sky conditions (CS)
Regardless of astronomical effect, on days whose sky has high atmospheric transmittance, the daytime solar irradiance variation is attributed only to atmospheric constituents (aerosols and water vapor, for example), mainly in the I D magnitude (Gueymard, 2012). Aerosols can reach levels that attenuate I D by approximately 70%, or more in extreme conditions (Ruiz-Arias et al., 2016).   H D values in the morning (from sunrise to noon) and afternoon (from noon to sunset) are higher than H G values for the same period. This can be caused by the atmospheric optical mass and the method of measuring the solar components that are different. While I D (H D ) is measured directly (with the pyrheliometer) pointed at the solar disk (following diurnal solar trajectory), I G (H G ) is measured with fixed sensor (pyranometer) on the horizontal surface. The daily average I G and I D were (687.2 ± 292.0 W m −2 ) and (787.0 ± 148.6 W m −2 ), respectively. The maximum I G value is close to that observed in Maceió  and higher than that found by Podstawczynska (2010). For six climatic zones in Nigeria and considering all types of sky cover condition, Chukwujindu and Julie (2017) found average values ranging from 6.30 to 28.8 MJm −2 .
In PRS, under CS conditions, daytime variation has a marked fluctuation caused by the passage of dispersed clouds in the atmosphere (Fig. 5b) Although it is characterized as clear sky day, the daily formation of transient clouds of the cumulus type is common at this time of year due to the proximity of the region to the Atlantic Ocean, which in some cases may develop into other types of clouds, both of horizontal or vertical development. The maximum I G and I D values were 1107.0 W m −2 and 905.8 W m −2 , respectively. The daily average was I G = 672.1 ± 329.5 W m −2 and I D = 702.4 ± 183.6 W m −2 . During this period of year, negative variation may occur due to the decrease of the solar radiation available at the top of the atmosphere and the increase of the water vapor content in the atmosphere, which is absorbed with greater intensity. Similar values for I G and I D irradiance was found for different sites in Portugal (Cavaco et al., 2016).
Also under CS conditions, for RS, the existence of greater oscillations and reduction of diurnal I G and I D values can be observed (Fig. 5c) Greater variations in values occurred in PDS during the daytime period, in which a sharp drop in the irradiance values was observed when I G decreased from (627.3 to 385.1 W m −2 ), and I D from (738.6 to 175.4 W m −2 ) (Fig. 5d). This oscillation is the result of the dynamics of cumulus clouds in the local atmosphere, because in this period (PDS), the water vapor in the atmosphere remains approximately constant. The maximum values observed for the day were I G = 1149.1 W m −2 and I D = 923.2 W m −2 , with daily totals H G d = 26.50 MJ m −2 and H D d = 24.52 MJ m −2 . It was observed that I D increases with the elevation of I G , revealing that I D is controlled by the variation of I G . Results similar to those from Maceió for I D were obtained by Padova (northern Italy) and Trisaia (Southern Italy) (Dugaria et al., 2015).

Analysis of solar irradiance under partially cloudy sky conditions (PCS)
Under PCS condition, the irradiance curves have larger fluctuations throughout the day, caused mainly by the dynamics of cumulus clouds in the atmosphere (Fig. 6a-d).
The maximum peaks I G and I D values were higher under PCS condition than on CS days. This is explained by the multi-reflections between the surface and the cloud bases, being phenomena typical of partially cloudy days, causing an increase of the descending reflection that increases the irradiance in comparison with cloud-free days . Souza et al. (2005) in a study on the solar irradiance for Maceió observed the occurrence of multiple reflections, confirmed by I G values very close to I 0 . In different places in the State of Alagoas / Brazil, it has been reported that this phenomenon is not uncommon and occurs on at least one third of the days in a given month (Andrade and Tiba, 2016 Porfírio et al. (2012). In the PRS, the irradiance that reached the surface was lower than in PDS, with daily average I G and I D values (maximum) of 507.6 ± 278.3 W m −2 (1099.6 W m −2 ) and 306.4 ± 241.6 W m −2 (859.0 W m −2 ), respectively (Fig. 6b)  The solar irradiance values in RS were smaller when compared to the other seasons, with a sharp decrease (between 09:00 am and 12:00 am) in I G from (673.7 to 302.2 W m −2 ), while I D decreases from (500.7 to 18.8 W m −2 ) (Fig. 6c). The irradiance remained low and increased to the maximum peak of I G (1015.5 W m −2 ) and

Analysis of solar irradiance under overcast sky conditions (OS)
Under OS condition, low I G and I D values are expected, since much of the solar irradiance cannot cross the Earth's atmosphere, being absorbed, reflected or scattered by clouds. In this condition, the clouds result in a reduction in I D values. Therefore, the absence of clouds causes the elevation of I G and I D in CS days, while in OS days, I D tends to zero and the I G is significantly reduced to smaller values (I G ≈ I d ). Thus, under OS condition, the daily I G values are greater than the daily I D values. Studies have shown that I D is much more sensitive than I G for changes in the amounts of clouds and aerosols (Ruiz-Arias et al., 2016). Moreover, in this sky cover, it is expected that the irradiance values for DS [I G = 362.4 ± 161.3 W m −2 and I D = 123.7 ± 188.2 W m −2 ] are lower than those observed in the other conditions (Fig. 7a). Peak I G and I D values were 732.7 W m −2 and 625.3 W m −2 , respectively. It was observed that the morning, evening and daily H G totals were one of the lowest values found, especially during the morning, whose I D was almost non-existent, caused by cloud attenuation. In PRS, the average daily I G and I D values were equal to 335.5 ± 200.3 W m −2 and 208.3 ± 226.6 W m −2 , respectively (Fig. 7b). The daily H G and H D totals were equal to 13.46 and 8.24 MJ m −2 , respectively. In RS, I D had values close to zero during the daytime period, the daily averages were I G = 265.0 ± 166.6 W m −2 (H G d = 10.47 MJ m −2 ) and I D = 49.6 ± 107.5 W m −2 (H D d = 1.94 MJ m −2 ), with daily maximum values of I G = 801.9 W m −2 and I D = 603.0 W m −2 (Fig. 7c). The daily totals were the lowest, since the selected day belongs to the rainy season and has low K t value. In relation to OS days in RS (Souza et al., 2005;Porifírio et al., 2012) found similar values with measurements in the same location from different years. The average daily I G and I D values were 328.6 ± 243.3 W m −2 (H G d = 13.18 MJ m −2 ) and 61.2 ± 126.3 W m −2 (H D d = 2.38 MJ m −2 ) and daily peaks reached 1089.5 W m −2 and 723.7 W m −2 , respectively (Fig. 7d). Study I G and I D Souza et al. (2005), Vilani et al. (2006) and Porifírio et al. (2012) found values with the same quantitative characteristics regarding the periods of greatest and smallest oscillations. The influence of cloudiness on I G and I D levels is remarkable. In addition, atmospheric water vapor has strong absorption in the region of the infrared spectrum, being able to reduce significantly the values of irradiances incident on the surface. The small differences observed along the analyzed periods show that energy totals are more affected by cloudiness than by seasonal variation, when compared with days of CS. In DS under CS condition, the maximum I h G value was 765.6 ± 100.0 W m −2 occurred between 09:00 am and 12:00 pm and was 728.2 ± 29.9 W m −2 (12:00 pm -03:00 pm), which were the highest values found for CS (   Figure 8 shows the average hourly global solar irradiation (H h G ) observed for all four seasons (obtained through the average irradiation of each hour interval). The diurnal variation among the different seasons is the same, increasing from morning until reaching maximum near noon and then falling until the end of the afternoon. In relation to this behavior, the hourly values tend to spread symmetrically to the solar half day. The largest curve amplitude is in DS, followed by PDS, PRS and RS. This behavior evidences the solar declination effect among seasons, the amplitude decreases as the day of the year distances from the summer solstice.  Souza et al. (2005), Marques Filho et al. (2016) and Tahir and Asim (2018). Although they are not located at the same latitude, the results of Maceió are similar to those obtained at sites in Nigeria by Osinowo et al. (2015), which found a uniform pattern in the distribution of H h G values, with peaks ranging from (15.01 to 12.01) MJ m −2 and with results observed in Saudi Arabia (AlYahya and Irfan, 2016).

Hourly solar irradiation
The daytime variation of H h G has a decrease after 08:00 am returning to increase soon after. This is due to the greater cloudiness in the morning, caused by the effect of local wind circulation (sea breezes), which are responsible for creating a zone of convergence near the coast (front breeze), contributing to the formation of cumulus clouds until near 01:00 pm, when it is verified the formation of an area of suppression of cumulus clouds related to the displacement of the zones of breeze subsidence and convergence (National Research Council, 1992;Silva, 2003 Pashiardis et al. (2017), who performed a statistical analysis of H D values, results found by Marques Filho et al. (2016) for Rio de Janeiro and for locations in Kenya (Kariuki and Sato, 2018), with values from satellite and two places of Morocco (Gairaa et al., 2017).

Frequency distribution of daily direct normal solar irradiance (I D d ) in the different sky cover conditions
In the frequency distribution of I D d for CS condition in the four seasons, it was observed that the I D d values in DS had greater occurrence between 400 and 600 W m −2 , comprising a relative occurrence rate of 68.8% of days, with higher occurrence of I D d for 440 W m −2 (Fig. 9a). Between 160 and 400 W m −2 , I D d maintained at a relative occurrence rate of 13.6% and from 600 W m −2 up to the maximum value (740 W m −2 ), the relative occurrence rate corresponded to 17.6%. I D d in PRS had relative occurrence rate of 65.91% between 400 and 600 W m −2 , between 257.5 and 400 W m −2 , the occurrence of I D d remained with relative occurrence rate of 15.69%, but from 600 to 700 W m −2 , the relative occurrence rate corresponded 18.19% of days (Fig. 9b). For RS, I D d had higher relative occurrence rate between 400 and 600 W m −2 , which corresponds to about 60.92% of days of this season and from 252.5 to 400 W m −2 , the occurrence reached 39.08% of cases (Fig. 9c). In PDS, I D d values between 385 and 635 W m −2 corresponded to half the relative occurrence rate of all values, the other half was between 235 and 385 W m −2 and the interval with the highest relative occurrence rate was between 385 and 435 W m −2 , which totaled 27.77% (Fig. 9d). For the city of Daejeon, in South Korea, Lee et al. (2017) showed higher relative occurrence rate for 50 W m −2 , followed by 850 W m −2 and with lower relative occurrence rate for 950 W m −2 .
Under PCS condition, I D d for DS showed higher occurrence between 250 and 450 W m −2 , totaling a relative occurrence rate of 55.43%, from 10 to 250 W m −2 , the relative occurrence rate was 41.30%, in the interval from 450 W m −2 up to the maximum value (I D d = 590 W m −2 ), the relative occurrence rate was 3.27% (Fig. 10a). In PRS, I D d had relative occurrence rate of 60.47% for the interval from 200 to 400 W m −2 (Fig. 10b). From 60 to 200 W m −2 , the percentage of I D d was 19.76% and from 400 to 600 W m −2 , corresponding to relative occurrence rate of 19.77%. The highest occurrence value of I D d was for the 300 W m −2 . In the relative occurrence rate histograms of I D d for RS (Fig. 10c), higher occurrence was observed close to 230 W m −2 , with higher relative occurrence rate (80%) between 38 and 308 W m −2 . In PDS, most occurrences of I D d were between 25 and 275 W m −2 , totaling a relative occurrence rate of 70.83%, between 275 and 675 W m −2 the relative occurrence rate of was 29.17% (Fig. 10d). In Seville -Spain, Moreno-Tejera et al. (2016) found that 42.4% of I D values F are higher than 600 W m −2 , with higher relative occurrence rate of high values close to the summer solstice of the Southern Hemisphere.
Under OS condition, the behavior of I D d is different from the other sky covers, since the higher relative occurrence rate for values smaller than 100 W m −2 as observed in DS (Fig. 11a), whose greatest occurrences were up to 188 W m −2 , corresponding to a relative occurrence rate of 71.42% and in the interval from 188 to 563 W m −2 , the corresponding relative occurrence rate is 28.58%. For PRS, all I D d measurements were not higher than 200 W m −2 , with 55% of the relative occurrence rate up to 100 W m −2 (Fig. 11b). In RS, the maximum value was 155 W m −2 , and up to 105 W m −2 , the relative occurrence rate was 80.64% and from 105 to 155 W m −2 , the relative occurrence rate was 19.36% (Fig. 11c). In PDS, the I D  values increased and the accumulated relative occurrence rate reached 100% up to a maximum of 488 W m −2 and 50% up to 338 W m −2 (Fig. 11d).

Final considerations
Cumulus clouds were mainly responsible for seasonal oscillation and irradiance attenuation, significantly reducing surface values. It was observed the phenomenon of multireflections that resulted in peaks and maximum values in the condition of partly cloudy days.
The instantaneous global and direct normal solar irradiance for seasonal periods showed maximum values close to noon, especially for clear sky conditions (global atmospheric transmittance, K t ≥ 0.60).
Higher oscillations were found in the intermediate seasonal periods (pre-rainy season -PRS and pre-dry season -PDS).
The daily totals of global and direct normal solar irradiation have greater variations due to the cloudiness than astronomical factors (seasonality), being the greatest values found, in the majority, in the morning during the dry and pre-rainy season.
The average daily totals of the global hourly solar irradiation were higher during the dry season, different from the direct totals that were higher in the pre-rainy season.
The lowest cloudiness levels were observed in the dry season, followed by pre-rainy, pre-dry and rainy seasons.
The relative occurrence rate of direct normal irradiance in the daily partition under conditions of K t ≥ 0.60 was greater between 400 and 700 W m −2 . Under conditions of 0.4 ≤ K t <0.6, I D d occurred more between 200 and 500 W m −2 and under conditions of K t < 0.4, it was below 200 W m −2 .
Therefore, according to the obtained results, it could be inferred that the patterns of solar incidence in the region of study are dependent on the cloudiness conditions. On the other hand, seasonality is a secondary factor that has little influence on the configuration of energy patterns. Thus, it was possible to characterize the distribution of direct normal solar irradiance for the region of Maceió, but there is still a need to intensify these studies for better understanding and application in several human activities, notably engineering, energy, agriculture, health and environment.