SUNSHINE, GLOBAL RADIATION AND NET RADIATION IN BRAZIL

This paper characterizes the spatial and temporal distribution of the sunshine, global radiation and net radiation in Brazil as well as the regional potential in the country, regarding these climatic parameters. Monthly and annual maps of these parameters, based on measured and estimated data from 204 meteorological stations distributed throughout the Brazilian territory, and temporal-spatial diagrams, derived from southnorth and west-east transects, show the trends in variation of these parameters and their relation to the various regional attributes of Brazil. These maps and diagrams contemplate both geographic aspects (vegetation, hydrography, orography, and geomorphology), and climatic elements (cloudiness and rain). Considering the absence of measured global radiation data, Angström’s equation of 1924 was used, which takes into account the sunshine data. An estimate of the radiation balance (net radiation) was obtained by Linacre’s equation of 1967. The maps of sunshine, global radiation and net radiation allowed the visualization of the spatial distribution of these elements. In the northern region, the sunshine is lower in areas with higher precipitation rates, such as around the Amazonas River mouth and in the Amapá State. Global radiation presents high values and little variation due to the high transmissivity of the atmosphere. Due to the uniformity of the relief and albedo, the net radiation also presents high values. In the northeast, high values of sunshine are explained by low cloudiness, especially in the semi-arid region (Caatinga / Sertão Nordestino). The maximum values of net radiation occur in the littoral. In the central-west region, in areas with greater amount of precipitation, the sunshine values are low. Global radiation and net radiation present similar values to those for the northern region. In southeastern Brazil, the distribution of sunshine is conditioned by factors such as relief, cloudiness and precipitation. Global radiation and net radiation are distributed more irregularly due to cloud cover, as in the case of the Rio Doce Basin, where the values are quite low. Net radiation is influenced by the albedo, which varies according to land use. In the South, all the elements exhibit DOI 10.5935/0100-929X.20170009 47698001 miolo.indd 49 28/05/18 11:20

orographic effects, which produces gradients from the coast towards the interior.Based on the spatial distribution of sunshine, global radiation and net radiation, Brazil's potential for solar energy can be verified as to qualitaty, quantity and consumptive use.This research also contributes to the agricultural planning regarding agroclimatic zoning, and crop forecasting; and to urban planning, in order to more adequately take into account the radiation balance concerning the ordering of vertical growth and the increase of green areas.

INTRODUCTION
The energy from the Sun, which reaches the surface of the Earth, is the most important factor in the development of the physical processes that generate weather and climate.
The sunshine is a qualitative measure of the solar energy, while global radiation represents the sum of the radiation coming directly from the Sun, plus the radiation diffused by the particles and gases of the atmosphere -it is therefore a quantitative measure.
The net radiation is the balance of the radiation, which is the result of the energy exchanges in the atmosphere conditioned by the flux of radiation emitted by the Sun -predominantly in short waves -and by terrestrial radiation -long waves emitted by the Earth's surface.This balance has great importance due to its environmental use: air and soil heating, latent heat of evaporation and biological processes.In addition, the radiation balance is a fundamental parameter in the climatic organization of urban and agricultural spaces.
The urbanized areas have specific characteristics that are important for their energy and water balances: wide variety in surface roughness, and large capacity to store heat.
The adequacy of the buildings of an urban area is derived from the local energy balance.In this case, the radiation balance will help in the orientation, type, format, number of openings, material, color of the painting, aiming to design the buildings and urban spaces in order to respect the climatic parameters and maximize the internal and external comfort of these environments for the human beings.
In agricultural areas the study of the energy balance allows the determination of potential evapotranspiration, a climatic element that represents the ideal rainfall index.These indices, together with precipitation ones, are important variables of the water balance.The results of the water balance, at regional scale, are fundamental for the studies of storage of water in the soil or in reservoirs.
There are few studies about sunshine and global radiation in Brazil.SERRA (1969) studied seasonal and annual sunshine variations; RATISBONA (1976) elaborated an annual chart of sunshine hours using selected stations ;and SERRA (1977) identified the regions of extreme values for the sunshine hours in Brazil.For global radiation there is only the work by NUNES et al. (1978), which presents monthly maps based on estimated data.
There is not yet any study on net radiation covering the whole of Brazil, since the few existing works are experiments at the micro and local level, developed in a short period of time.
Therefore, it is necessary to overcome the lack of knowledge of these elements in the spatial scale of the Brazilian territory.Due to its continental dimensions, coupled with the relatively high cost, there is great difficulty in installing instruments for the measures of sunshine, global radiation and net radiation.
The main objectives of this work are: • To contribute to the knowledge of the average monthly and seasonal variations of solar radiation, global radiation and net radiation in Brazil; • To determine the regional potential of the country regarding these climatic parameters; • To estimate the net radiation based on a geographical methodology, with emphasis on spatial analysis of the Brazilian territory; Due to the absence of measured global radiation data, the estimation was based on sunshine data using a method proposed by ANGSTRÖM (1924).
In Brazil there is not a network of instruments of net radiation, due to the high price of these equipments.Some researchers from universities' laboratories have usually estimated these parameters using meteorological data from stations.The most used formulation was established by BRUNT (1939) and adjusted by PENMAN (1948).In our case, it cannot be used due to the few relative humidity data.
The best solution found for this problem was to use the Linacre's equation of 1967, which is easier to apply because it does not require relative humidity data.Its accuracy is equal to or slightly higher than that of Brunt-Penman's formulation, considering the spatial and temporal scale of the study.
The most important results of this study can be summarized: • Better knowledge of the spatial and temporal distribution of these parameters; • Contribution to the study of the influence of geographical factors on the variation of spatial distribution of these elements; • Evaluation of the Brazil's potential for solar energy as to qualitaty, quantity and consumptive use.
In addition, they may be applied for the following purposes: • Urban planning: establishment of norms for the orientation of roads and streets, dimensioning and height of commercial and industrial buildings and houses for receiving the right amount of light and heat; • Tourism feasibility studies of recreation and leisure areas, considering the Sun exposure.Preservation and introduction of green areas in the cities, with the purpose of establishing a better balance of energy of the urbanized areas; • Agricultural planning: adequacy of cultivars to the photoperiod, agricultural zoning, management and adaptation of crops, crop forecasting, determination of potential evapotranspiration by the Penman's method (1948) and drying of cereals; • In the field of technology: environmental heating, heating of fluids for industrial use, steam generation, window and awning window designs, water heating in homes and buildings (hotels, hospitals, clubs, schools, etc.), distillation of seawater or brine, concentrators for heat production, photocells for the production of electricity.
Our study has some limitations, mainly due to the difficulty of obtaining data, the low and irregular density of the meteorological network and the heterogeneity of the observation periods.
Some weather elements, such as air temperature, relative air humidity and global radiation, have failed and absent records in many stations.
In the case of sunshine, there is a greater amount of data, since the heliograph is an instrument of easy handling and not very difficult interpretation of its records.The more labor-intensive interpretation, requiring the use of manual or digital planimeters or readers, makes global radiation a meteorological element with few data series; in addition to the high price of the recording instrument, which restricts its use in our country.
There are practically no instruments installed for net radiation, which also occurs in other countries.The difficult maintenance of net radiometers requires researchers to take a number of special precautions which, if not adopted, could affect the quality of the measurements.
Due to the continental dimension of Brazil and the difficult accessibility of certain regions, the meteorological network does not have adequate density despite the efforts of the responsible entities.
The figure 1 presents the methodological approach and stages of the research, from literature review, data collection and selection, to spatial and temporal analyses of sunshine, global radiation and net radiation.

Introduction
The sunshine is defined as the number of daily hours of brightness of solar disk.It is influenced by geographic and astronomical factors: latitude and inclination of the Earth's axis of rotation to the ecliptic.
For practical purposes of study, the sunshine can be distinguished in three aspects: • Theoretical or maximum possible (N) sunshine, which depends on astronomical factors and can be calculated by trigonometric formulas that provide the duration of the day; • Actual or effective sunshine (n), which is recorded, being a function of cloudiness; • Relative sunshine or percentage of sunshine ( n N ) is the ratio between the actual and the theoretical sunshine.

Data
The actual sunshine (n) is obtained from the reading of the burn marks made by solar rays into the diagrams (tapes) of the Campbell-Stokes sunshine recorder.
This instrument consists essentially of a glass sphere -about 10 cm in diameter -concentrically mounted on a section of a spherical arc, allowing that the sun's rays focus on the diagram.The sphere support has an adjustment system for latitude.
When installing the instrument, it is necessary to take into account that it is well oriented in azimuth and level and free horizon in 360º.
The diagrams for sunshine recording must be of good quality and printed in shade-blue color, which absorbs solar radiation.There are three sizes of diagrams, which are used according to the season: long curved (summer), short curved (winter) and straight (spring and autumn).The records should be done with an accuracy of 0.1 hour (6 minutes).
In Brazil, the main data repository is the Instituto Nacional de Meteorologia (INMET), which has a network of stations that covers practically all the national territory.There are also networks of stations and isolated stations, which belong to state agencies and universities.In this work all available data (Table 1) were used due to the low density of the network.47% of the stations used had the complete series of the period 1931-1960 (30 years), and 57% had more than 10 years of records.Unfortunately the series are not continuous.Non-consistent data were eliminated (34 stations of a total of 231).The location of the stations is shown in figure 2 and table 2. Abbreviations in table 1 (References): INMET -Instituto Nacional de Meteorologia -Ministério Agricultura (INMET 1931-1960, 1968).
The theoretical sunshine (N) consists of the maximum possible number of daily hours of brightness solar disk.It is the amount of time between sunrise and sunset.The determination of N is based on the trigonometric formulas of the astronomical triangle.This calculation requires the latitude of the place and the declination of the Sun.The latter is published in astronomical yearbooks.
There are tables that provide the times of sunrise and sunset, such as those of PEREIRA et al. (1971).To calculate the theoretical sunshine, we use these tables, applying two corrections: a) Atmospheric refraction correction, in which the following average values were considered for Brazil: Mean temperature = 20 °C; average altitude = 400 m, which corresponds to an average atmospheric pressure of 725 mmHg (967 hPa).The value is additive: 2 • 34' = 68' (sunrise and sunset); b) Correction due to the mean apparent diameter of the Sun.Astronomically it is considered the center of the disc of the star, at sunrise and at sunset.This disc has an average apparent diameter of 32' (ie, 16' at sunrise + 16' at sunset).
The sum of the both corrections gives the following result: • Refraction correction: 2 • 34' = 68' • Correction due to the diameter of the solar disk: 2 • 16' = 32' • Total value (additive): 100' Since one hour corresponds to 15° (= 900'), 100' is equal to 0.111 h, or approximately 6 min.This value was added to the tables of PEREIRA et al. (1971).These corrected tables are coherent with the Smithsonian Meteorological Tables (LINACRE 1969a).
We thus obtained the duration of the daylength (N . ) for each season and each month.N . of day 15 was considered representative of the month.February was considered with 28 days.
The monthly total of theoretical sunshine N was calculated by the equation: x number of days of the month The sunshine ratio ( n N ) (dimensionless) was obtained by division of the actual sunshine values (n) by the theoretical sunshine (N).This parameter is important for the estimation of global solar radiation by Angström's method (1924).

The cartographic treatment
Monthly charts were produced using a base map from IBGE, with a scale of 1: 5,000,000, in azimuthal conformal projection.Isocontour maps of sunshine (monthly and annual) were traced based on 197 stations data, considering the relief, natural vegetation, hydrography, geomorphology, cloudiness and rain.
Spatial-temporal diagrams (abscissa axis = meteorological stations, ordinate axis = months of the year) were generated for transects (southnorth and west-east) (Figure 2).The selected stations along the transects are shown in table 2. This method, applied by SNYTKO (1978) for the study of geosystems, provides a visualization of the spatial-temporal trends of sunshine in Brazil.

Results and discussion
The spatial distribution of the sunshine can be visualized in the annual and monthly maps (Figures 3, 4) (see APPENDIX for station data and radiation budget results -available online at http://dx.doi.org/10.5935/0100-929X.20170009).It depends on several factors that are influenced by regional characteristics.The two spatial-temporal diagrams (south-north and west-east, Figure 5) provided a better understanding of the variation over time and space, and also the influence of geographical factors on the sunshine.
In the northern region of Brazil, the effects of latitude are less pronounced due to the proximity of the equator.The influence of the orography is also not evident, because of the relief has low expression.The sunshine distribution is similar to the rainfall chart.In general, the sunshine is lower where it rains more.The lower values of sunshine occur in the first half of the year, when precipitation is higher (Figures 3, 4).
In the northeast region, the sunshine values are high due to the low cloudiness.The relief in this region is responsible for these variations, mainly in the valley of the São Francisco River, where the values increases from the coast to the interior.
In the central-west region, the low orography does not play an important role in the sunshine.North of this region, the values are smaller due to the greater cloudiness and precipitation.
In the southeast region there is a strong influence of the orography; this effect is added to the existence of frontal cloudiness.The sunshine smallest values occur in the region of the Rio Doce Valley (MG/ES) and the Serra do Mar.In the latter one, precipitation reaches the maximum values in Brazil.
The relief and cloudiness are also the main factors for the sunshine variations in the south region.The cloudiness is greater in the coast of Paraná and Santa Catarina, which corresponds to the low number of hours of sunshine in this region.
The effects of the orography and cloudiness could be visualized in the spatial-temporal diagrams.
The south-north transect (Figure 5) extended from the Uruguay border to the coast of the Ceará State, and shows the following compartmentation: • The west-east transect (Figure 5) extended from Benjamin Constant (AM) to Recife (PE), and shows the following compartmentation: • From the Colômbia border to the mouth of the Juruá River: sunshine values are almost the same throughout the year; • From the mouth of the Juruá River to the mouth of the Amazon River: the lowest values of sunshine correspond to the rainy season (December to April), while the highest ones concentrate in the rest of the year; • From the mouth of the Amazon River to the Piauí State: the lowest values occur from February to April, whereas the highest ones occur from August to November; • From the State of Piauí to the coast of the Pernambuco State (Recife): there is a great irregularity from place to place, due to the orography.Comparing this study with the previous ones, we can observe that the monthly maps of January and April, and July and October (Figure 4), are similar to those of SERRA (1969).The main difference is that this author did not have many stations and had to interpolate lines in the monthly maps.The annual map (Figure 3) is very similar, except for some regions, due to the greater number of meteorological stations in the present study.
In general, the annual map by RATISBONA ( 1976) is very similar with the one of the present study, which is more detailed due to the greater number of stations.
Our monthly sunshine maps are similar to the SERRA (1977)'s maps.They agree approximately with figure 4, however, we used a greater number of stations and years of observation, and the timespace diagrams for a more accurate analysis.At the regional scale, comparing with the maps by AZEVEDO et al. (1981) for the northeast region and ORSELLI (1982) for the Santa Catarina State, we can observe that both are more detailed due to the greater number of stations analyzed.But, in general, there is a great similarity between these maps and the present ones.

Introduction
The amount of solar energy that reaches the earth's surface is called global radiation.It is composed by radiation that comes directly from the solar disk (direct radiation) and from diffuse radiation.The latter is the fraction of the extraterrestrial radiation that suffers dispersion in the atmosphere.
The radiation flux that falls perpendicularly on a unit area surface at the upper boundary of the atmosphere at the mean distance between the Sun and the Earth is called the solar constant.
The value of this constant, according to the best determinations is: 1.94 cal cm -2 min -1 or 1.94 ly, or 135.3 mW cm -2 (± 1.3%) For practical purposes solar radiation can be studied in three ways: • Extraterrestrial radiation or radiation at the top of the atmosphere (Q o ): it is the maximum possible theoretical radiation for a given day and place.Their values can be found in tables.In Brazil, they were calculated by SALATI et al. (1967); • Global radiation measured (Q g ) or estimated at the soil level, whose data are published by the institutions responsible for the collecting; • Radiation ratio ( At the local scale, most of the papers established the relationship between solar radiation and global solar radiation in order to determine the linear regression equations for the estimation of the radiation, when there is only sunshine data.This estimation was initially established by ANGSTRÖM (1924) and then, with some modifications, by PENMAN (1948), BLACK et al. (1954), GLOVER and McCULLOCH (1958), DAVIES (1965) andLINACRE (1969b).

Data
For measurements of global radiation, the most used instrument is the actinograph of Robitzsch-Fuess, whose principle of operation is the differential heating of bimetallic plates.Two are painted in white and one in black.The difference in plate expansion is proportional to the differential absorption of incident solar radiation.
Actinographers have a special glass dome for the protection of sensitive elements.A mechanical system of levers transmits to a pen the variations of the radiation.The record is made on a diagram that is placed on a clockwork drum, with daily rotation.The sensitivity of this instrument is of the order of 5-10%.
Another instrument used for global radiation measurement is the Eppley Pyranometer; but its use is more restricted due to its high cost and difficult maintenance.
The actinograph diagrams are interpreted by integrating the area.This requires the use of planimeters, and manual or digital readers.At the end of the process is provided the daily total of global solar radiation (ly day -1 ).
In Brazil, due to the low density of the network of stations, we used all available data from INMET and other institutions (Table 3).46.4% of them had 5 to 18 years of data record.
The total solar radiation reaching at a horizontal surface per unit area at the top of the atmosphere (Q o ) is a function of the latitude of the place (Φ) and the declination of the Sun (δ): Q o : solar radiation at the top of the atmosphere on a horizontal surface per unit area (ly day -1 ) π: 3.1416 We applied corrections for the calculated value due to the atmospheric refraction and the diameter of the Sun.The sum of the both corrections gives an additive of 0.1 h (6 min).To avoid all these calculations, we used tables generated by SALATI et al. (1967) for Brazil that provide the Q o indexes for all the year and for the latitudes from 10º N to 40º S. The value of day 15 is taken as representative of the month.The The most well-known formulation was proposed by ANGSTRÖM (1924): where: The regression line is given by: The least squares method was used for the determination of a and b.In addition to the parameters a and b, the correlation coefficient (r) between the variables and the coefficient of determination (r 2 ) were obtained from a total of 65 regression lines (Table 4).
For stations without actinograph records, but with sunshine data from sunshine recorders, global radiation was estimated using the values of a and b from the nearest station or from the same or similar climate region.Vegetation, topography, altitude, etc. were still taken into account for this estimate.

The cartographic treatment
Monthly maps were produced using a base map from IBGE, with a scale of 1: 5,000,000, in azimuthal conformal projection.Isocontour maps of global radiation were traced based on 204 stations data, considering the relief, natural vegetation, hydrography, geomorphology, cloudiness and rain.Spatial-temporal diagrams (abscissa axis = meteorological stations, ordinate axis = months of the year) were generated for transects (southnorth and west-east) (Figure 2).The selected stations along the transects are shown in table 2. This method, applied by SNYTKO (1978) for the study of geosystems, provides a visualization of the spatial-temporal trends of global radiation in Brazil.

Results and discussion
The spatial distribution of the global solar radiation can be visualized in the annual and monthly maps (Figures 6, 7) (see APPENDIX available online).The two spatial-temporal diagrams (south-north and west-east, figure 8) provided a better understanding of the variation over time and space, and also the influence of geographical factors on the global radiation.The monthly and annual spatial distribution of this parameter is conditioned by several factors and varies according to the characteristics of each region.These variations are somewhat different from those of sunshine.
The regions with the maximum values of sunshine do not coincide necessarily with those of higher global radiation.In the northern region of Brazil, the effects of latitude are less pronounced due to the proximity to equator.Although the cloudiness of this region is relatively high, the transmissivity is high.The global radiation has minimum values in the Amapá State and the Amazonas River mouth (less than 350 ly day - 1 ).In the rest of this region the values are above 400 ly day -1 .The minimum values are found in regions where there is higher cloudiness and lower atmospheric transmissivity.
In the northeast of Brazil, the highest values of global radiation occur in the semi-arid region (Caatinga), due to the low cloudiness and high transmissivity of the atmosphere.
In the central-west region, the values are similar to those of the Amazon region.The lowest values occur in the southeast of the Mato Grosso do Sul State, whereas the highest ones in the most part of the Mato Grosso State and in the region of the Mato Grosso's Pantanal wetlands.
The variations of the global radiation in the southeast region are due to the presence of  (1) SÁ (1973) (2) TUBELIS et al. (1977) cloudiness, which increases by the orographic effect of the mountain ranges.The lowest values occur in the Rio Doce Valley, where the cloudiness is persistent and strong.In addition, transmissivity is low in this part of Brazil.
In the southern region, the Paraná State and northern Santa Catarina present low global radiation (Q g ) values, due to the strong cloudiness and precipitation, besides the low transmissivity.The highest values of this region are located along the coast of these states.Due to the orography, the values decrease from the coast to the interior.
The sunshine is a function of the amount of cloudiness, whereas global radiation varies according to the amount and type of clouds, and also with transmissivity.
(3) CERVELLINI et al. (1966) (4) TARIFA (1972) On the other hand, the transmissivity is influenced by the latitude (which affects Q o ), the amount of water vapor and particles in suspension.
The south-north transect (Figure 8), which extends from the Uruguay border to the coast of the Ceará State, shows the following compartmentation: • From the Uruguay border to Uberaba-MG: the maximum values of global radiation occur in the summer and the minimum values in the winter.In the mountain regions there is an influence of the orography; • From Uberaba-MG to Pirapora-MG: there are no major differences between the maximum and minimum values; however, the absolute minimum values occur in the winter; • From Pirapora-MG to Caetité-BA: irregular distribution with minimum values in the winter; there is an influence of the orography; • From Caetité-BA to Bebedouro-PE: the distribution is very irregular, with maximum values in the summer and minimum ones in the winter; • From Bebedouro-PE to the coast of Ceará: the distribution is relatively regular and uniform.
The west-east transect, from the Javari River (Peru border) to Recife-PE, shows the following compartmentation (Figure 8): • From Javari River-AM to Arumanduba-PA: maximum minimum values in the summer and the winter, respectively.The regularity is due to the latitude and uniform topography (with relief of the order of 200 m); • From Arumanduba-PA to Teresina-PI: the distribution is very irregular; the maximum values occur in the second half of the year due to the rainfall regime; • From Teresina-PI to Recife-PE: the relief is rugged.The maximum values occur from August to April and the minimum ones occur in the winter.Variations in this pattern are due to local effects, although the values are not very different throughout the year.
There are some similarities between this work and the study by MOTA et al. (1977), at    (Figure 2).See identification of the stations (numbers along the profile) in the table 2.
annual level.Both maximum values occur in the semi-arid region (Caatinga).NUNES et al. (1978) produced monthly maps of estimated global radiation based on the formulation of BENNETT (1975).There are some similarities with the present work, which is more evident for the maximum values than the minimum ones.We used measured values from 99 stations and estimated from other 105, while NUNES et al. (1978) used only estimated data from 180 stations.
VILLA NOVA & SALATI (1977) reported a 12% error in their global radiation data available in Brazil.In this analysis we found percentage errors of the same order of magnitude.
In this work, we performed a study of the frequency of the maximum percentage deviations between the measured and the estimated global solar radiation, using the Angström's equation (Table 5).Of the 65 meteorological stations, 56 had maximum percentage deviations below 10.0%.

Introduction
The net radiation is the balance of the radiation.This is the result of the energy exchanges in the atmosphere, conditioned by the fluxes of radiation emitted by the Sun -predominantly in short waves -and by the terrestrial radiation emitted by the ground surface (long waves).
From the solar radiation that reaches the ground surface, part is reflected by the surface and the rest is absorbed.The higher the albedo (reflectivity), the lower radiation is absorbed and vice versa.
The importance in studying the net radiation (Q n ) is in the consumptive use of this energy.This is dissipated or consumed in the following processes: air heating or sensible heat (H), latent heat of evaporation (LE), soil heating (G) and biological processes (photosynthesis and others) (F).
The equation that summarizes the consumptive use of the net radiation is: The heat flux in the soil (G) depends on the thermal capacity and the conductivity of the soil.Experimental measurements show that, in determining the radiation balance in one or more weeks (our case), the G value is very small and can be neglected.
The amount of energy used in the photosynthetic and biological processes is very small, of the order of 1-2% of the total, being also negligible.
Because the values of G and F are very small, in practice, the consumptive use of net radiation is: The amount of heat to evaporate 1 mm of water is called latent heat of evaporation (LE).This parameter varies slightly with the temperature, being of approximately 59 calories to 1 mm of water.
Approximately 70-80% of the available net radiation is consumed in the evapotranspiration process.The remainder corresponds to the sensible heat that heats the soil and the air.
The laws governing the flow of heat in gases cannot be applied to predict the sensible heat flux in the atmosphere, because this is an open system.The air flow above the soil surface causes it to be continually renewed and blend with the higher layers.
The measurement of H is impossible in practice.To solve this problem, we used the Bowen's ratio to calculate the LE value.
The determination of the net available energy is indispensable for the calculation of evapotranspiration for irrigation, water balance and organization of agrarian and urban spaces.
By studying the work of BRUNT (1939) about long-wave balance (effective terrestrial radiation), PENMAN (1948) established the following equation for the determination of the net radiation: Where: Q g .(1 -a) refers to the shortwave balance, which is easily obtained.The long-wave balance (R b ) was focused on several works (LONNQVIST 1954, MONTEITH 1961, SWINBANK 1963and LINACRE 1967).
In Brazil there is no study about net radiation at national level -only at regional, local and microclimatic scales.At the regional scale, we can cite the following works: VILLA NOVA et al. (1977) estimated Q n values for the Amazon region using the PENMAN method (1948), for the study of potential evapotranspiration.JOHNSON (1982) compared the methods of Penman and Thornthwaite for the determination of evapotranspiration in the central-western region of Brazil; this work presents an estimate of the net radiation for this part of the territory.ORSELLI (1982)  -Australia.These instruments must be connected to the potentiograph, in order to record the net radiation.
The working principle of the former is similar to that of the Eppley pyranometer for global radiation.It consists of two sets of thermoelectric pairs (differential thermopile), mounted on the upper and lower parts of a black plate, which absorbs the global radiation at the top and the effective radiation at the bottom.
The thermal energy of the sensors is dissipated by a fan, which passes a current of air over the sensitive elements.The problem is the impossibility of taking measurements on rainy days.
The "Net Pyrradiometer" consists of a thermopile in the form of a square plate, covered on both sides by polyethylene hemispheres.The hemispheres remain inflated due to the forced circulation of air or nitrogen that prevents the condensation of the water vapor and homogenizes the temperature inside the instrument.Due to the protection of polyethylene, the data acquisition is not subject to rainfall interference.
In Brazil, the nitrogen feed is replaced by an aquarium aerator.The compressed air from the aerator passes through a container filled with silica gel before being injected into the net radiometer.The circulation recommended by the manufacturer is controlled by the adjustment of the stroke of the aerator.

Estimation of terrestrial effective radiation
Due to the lack of stations for measuring the terrestrial effective radiation (R b ), it is generally estimated.In this work we adopted the formulation proposed by LINACRE (1967)  (1.191 .10 -7 cal cm -2 day -1 K -4 ); T a : mean air temperature (K).
The correction of the effective terrestrial radiation to a clouded sky (R b ) is given by the expression (cal cm -2 min -1 ): where [g + (1 -g)] .n N corresponds to the correction for cloudy skies; g is a parameter related to the height of the clouds and varies according to the author: 0.10 (PENMAN 1948); 0.20 (KRAMER 1958); 0.24 (IMPENS 1963) and 0.30 (FITZPATRICK 1965apud LINACRE 1967).In this work, we used the average value (0.20) for the equation: In numerical values: R b = (0.245 -0.158 .10 -10 .T a 4 ) .[0.20 + (0.80 .n
All of the stations used in this work (175) had sunshine ratio data, but only 104 stations had the average air temperature data.To solve this problem, we used an estimate based on the work by VASCONCELLOS & TARIFA (1983).
In addition to the mentioned parameters, we used relative air humidity data (%) from the period 1931-60 of all stations, in order to compare the Linacres's equation of 1967 with the Brunt-Penman's formula.

Albedo estimation
The surface reflecting power, or albedo, was classified in three categories: albedos of natural vegetation, albedos of agricultural crops, and albedo of urbanized areas.For the natural vegetation, we adopted the types established by HUECK (1972) in his South American chart (21 types).Agricultural crops were divided into permanent crops (coffee and sugar cane) and annual crops (rice, cotton, corn, soybeans and wheat).The following metropolitan areas were considered as urban areas: Belém-PA, Belo Horizonte-MG, Brasília-DF, Curitiba-PR, Fortaleza-CE, Porto Alegre-RS, Recife-PE, Rio de Janeiro-RJ, Salvador-BA, and São Paulo-SP.
We adopted albedo values from the literature: OGUNTOYINBO (1970), STANHILL et al. (1966), GEIGER (1975)  For the albedo of the meteorological stations it was taken into account the main type of vegetation in their areas.There is certain homogeneity of (natural) vegetation in regions such as the Amazon and the semi-arid (Caatinga), but in the others our task was made very difficult by the intense land use.In areas where natural vegetation was replaced by crops, we obtained the albedo values for the meteorological stations based on the predominant culture in each municipality (IBGE 1977).
In this way, we obtained the albedos for 175 stations in Brazil (mean value: 0.19), which were used for the net radiation calculus.

Estimation of net radiation
The equation that represents the net radiation is: Where: Q n : net radiation or balance of radiation (ly day -1 ); Q g : global radiation (ly day -1 ); Q g (1 -α) = Q a : global solar radiation absorbed by the surface, i.e.Q a correspond to the short-wave balance; α: surface albedo; Q L↓ : downward long-wave radiation (ly day -1 ); Q L↑: upward long-wave radiation (ly day -1 ); (Q L↓ -Q L↑ ) = R b : corresponds to long-wave balance, or effective terrestrial radiation (1y day -1 ); So, finally, we have: Then, we used the equation of LINACRE (1967) [Eq.9] in [Eq.11]: . 1440 [Eq. 12] This formula is quite simple and takes into account four parameters: global radiation (measured or estimated); the surface albedo (determination based on measurements), sunshine ratio (n: measured and N: calculated) and mean air temperature (measured or estimated).

The cartographic treatment
Monthly and annual charts and spatialtemporal diagrams of net radiation (Q n ) were produced using the same procedure for sunshine and global radiation.Isocontour maps of net radiation were traced based on 175 stations data, considering the relief, vegetation, hydrography, geomorphology, cloudiness and precipitation.The cloudiness values were based on surface observations and satellite data (MILLER & FEDDES 1971).

Results and discussion
The spatial and temporal distribution of the net radiation (Figures 9, 10) is conditioned by several factors that vary according to the peculiarities of each Brazilian region.
The north and center-west regions have high values, which varies a little from month to month.This is due to the uniformity of relief, albedo and little effect of latitude.The maximum values of the northeast region generally occur on the coast, from Rio Grande do Norte to southern Bahia.See identification of the stations (numbers along the profile) in the table 2. LINACRE (1969a and1978), the precision of the estimates is about 20%.The results of this research are within the generally accepted limits.
There are few series of net radiation data in Brazil.OMETTO (1968) obtained a data series for the agricultural year of 1966-67 in Piracicaba-SP.By adopting the 0.20 albedo employed by that author, we applied the LINACRE (1967) formula for the Piracicaba data at the same agricultural year.We found a correlation of 0.95 between the values of estimated net radiation and OMETTO measurements (Figure 12).By using the Brunt-Penman's formula and the same data from OMETTO (1968), we found a correlation coefficient of 0.94.Table 7 shows OMETTO measurements (1968)  Based on these results, we can affirm that the Linacre's equation of 1967 is valid for the estimation of the net radiation.At the monthly scale, this approach evaluates Q n with equal or slightly greater precision than the classic Brunt's equation, modified by PENMAN (1948).

CONCLUSIONS
Based on the results obtained in the charts and time-space diagrams presented in this work, the following conclusions are valid: 1) The use of Angström's equation of 1924 for the estimation of global radiation was within the precision required by the temporal and spatial scales of this work.
2) When used for determination of the effective terrestrial radiation, the Linacre's equation ( 1967) was comparable to the Brunt-Penman's equation.
3) In some regions, the irregular density of the station network hinders larger scale studies.
4) The geographical factors, such as the relief and land use, have an important influence on the parameters, as observed by the analyses of the maps and temporal-spatial diagrams.
5) The cloudiness, rainfall and transmissivity of the atmosphere are the most important climate parameters for the sunshine, global radiation and net radiation.8) Although having areas with low values, the general potential of our country is very high: 2522 h year -1 of sunshine (~ 7.0 h day -1 ); 427 ly day -1 of global radiation; and 237 ly day -1 of net radiation (mean values of all seasons).9) Comparing with the measures by OMETTO (1968) in Piracicaba, the Linacre's equation of 1967 was shown to be quite satisfactory with a correlation coefficient of 0.95.
10) The spatial temporal diagrams show the different behavior of sunshine, global radiation and net radiation along the south-north and west-east transects in Brazil.
11) The results of this research work can be applied to the planning of urban and agrarian spaces at the regional level.
12) The elements of the radiation balance can be used at the local and regional scales.
13) The radiation balance varies from one place to another and throughout the year in the southeast and south regions, due to the anthropic action (differentiated land use).
14) A pronounced gradient was observed for the values of global radiation and net radiation in the south and southeast regions, due to the orography.
15) Due to the limitations imposed by the amount of data and the irregular distribution of the network of stations, the maps of sunshine, global radiation and net radiation presented here should be considered as valid estimates to improve the knowledge of the climate realities at the regional scale.
16) In this work the values for global radiation and net radiation were expressed in langley (ly day -1 ).To be transformed into the unit W m -², it is necessary to use the equation: W m -² = ly * 0.485.

FIGURE 2 -
FIGURE 2 -Location of the meteorological network used in this work and the transects for the temporal-spatial analysis.
From the Uruguay border to the southern of the São Paulo State: high values from October to March, decreasing in winter; • From the southern part of the São Paulo State to the Triângulo Mineiro (MG): there are no major variations during the months of the year; summer is the season with the lowest values; • From the Triângulo Mineiro (MG) to the south-central of Bahia State: highest values of sunshine in winter (May to August), and lowest values in the summer; • From the south-central area of Bahia State to the coast of Ceará State: characterized by irregularity throughout the year; the lowest values occur in the winter, which is the rainy season.The relief also produces local effects.

FIGURE 5 -
FIGURE 5 -Temporal-spatial variation of the sunshine along the south-north (A-B) and west-east (C-D and E-F) transects (Figure2).See identification of the stations (numbers along the profile) in the table 2.
day in minutes) = [0.1333 .arccos -(tan δ .tan Φ )] .60 (radiation ratio) indicates the percentage of energy received at the top of the atmosphere that reaches the soil surface.It represents the atmospheric transmissivity over the site of observation.The Q g Q o ratio was obtained by simple division and its result (dimensionless) was rounded to the second decimal place.When no global solar radiation data are recorded, estimates are taken from meteorological data.
global solar radiation at ground level (ly day -1 ) Q o : radiation at the top of the atmosphere (ly day -1 ) n N : sunshine ratio a, b: statistical parameters of the regression line

FIGURE 8 -
FIGURE 8 -Temporal-spatial variation of the global radiation along the south-north (A-B) and west-east (C-D and E-F) transects(Figure2).See identification of the stations (numbers along the profile) in the table 2.
established monthly net radiation maps for Santa Catarina State, using the modified Brunt-Penman's formulation.At the local scale: VILLA NOVA et al. (1966) established the radiation balance for Piracicaba-SP.OMETTO (1968) studied the relationships between net radiation, global radiation and sunshine, based on a year of measurements.TARIFA & MONTEIRO (1972) calculated the radiation balance for the region of Presidente Prudente-SP.MOTA (1976) established equations for Pelotas-RS.MORAES et al. (1977) studied the types of weather and radiation balance in the city of São Paulo, using IAG data.At the microclimatic scale, VILLA NOVA (1973) established the energy balance in rice cultivation in Campinas-SP.4.2 Methodology 4.2.1 Material and methods The most widely used net radiometers for the measurement of net radiation are: "Net Exchange Radiometer" devised by GIER & DUNKLE (1951) and constructed by Beckman and Whitley; and the "Net Pyrradiometer" idealized by SCHULZE (1953) and manufactured by Middleton & Co. Ltd.
that used the Swinbank's equation of 1963 for longwave radiation flow downwards, with clear sky, adding the effect produced by the cloudiness.For completely clear sky conditions, LINACRE used: effective terrestrial radiation with clear sky; σ: Stefan-Boltzman constant

FIGURE 11 -
FIGURE 11 -Temporal-spatial variation of the net radiation along the south-north (A-B) and west-east (C-D and E-F) transects (Figure 2).

FIGURE 12 -
FIGURE 12 -Comparison between the estimated values obtained by Linacre's equation (1967) and the measurements obtained by OMETTO (1968) for Piracicaba -SP.

6)
In general, the north, northeast and centralwest regions present the highest values of sunshine, global radiation and net radiation.7) The minimum values of sunshine, global radiation and net radiation are located in the Rio Doce Valley (MG/ES) and central-west of Paraná and Santa Catarina.

TABLE 1 -
Number of meteorological stations per institution.

TABLE 2 -
(cont.)Location and identification of meteorological stations selected for the study.

TABLE 3 -
Meteorological stations used for the study of global radiation.

TABLE 4 -
Stations with a and b values for Angström's formula.

TABLE 5 -
Absolute and relative frequency of maximum deviations between measured and estimated global solar radiation, using the Angström's formula.

TABLE 7 -
Relative deviations between the net radiation measured by OMETTO (O) and those estimated by the equations of LINACRE (L) and BRUNT-PENMAN (B).