Pyranometer and Pyrheliometer

SOLAR RADIATION by A.P.Sastry, Updated: March 2011 11

The sun, which is about 1.495 X 10 m away from the earth, is a sphere with a diameter of 1.39 9 X 10 m consisting of intensely hot gaseous matter. As observed from the earth, the sun rotates on its axis once about every four weeks. The sun has an effective black body temperature of  6 6 5762 /5777 K and the core temperature is estimated to be lying between 8 X 10 and 40 X 10 K. Several fusion reactions occur in the interior of the sun producing energy at a temperature of  many million degrees. This energy, with successive emission, absorption and re radiation involving radiative and convective process is transmitted to the surface.

Fig. 1 The sun earth relationship relationship The features of the sun surface are granules, small, dark areas called pores. Photosphere is the outer layer after convective zone, which is the source of the most of the solar radiation. The sun's surface is opaque, its constituent gases are strongly ionized and are able to absorb and emit a continuous spectrum of radiation. Solar atmosphere, which is transparent, is at the outside of the photosphere. This can be observed during total solar eclipse. A reversing layer, a layer of cooler gases, which is several hundred kilometers deep, exists above the photosphere. Another gaseous layer surrounds this lower density and higher temperature than that of photosphere, called chromospheres of depth of about 10,000 km. Then still farther exists corona, which is of low density and very high temperature of  6 10 K. In fact, the sun does not function as a blackbody at a fixed temperature radiating heat, but emits solar radiation as a combined result of several layers emitting and absorbing radiation of  various wavelengths. The earth is a sphere flattened at the poles and bulging in the plane normal to the poles, which is an oblate spheroid shape. However, earth is regarded as a sphere with an approximate diameter 7 of 1.22 X 10 m. The earth rotates about its own axis, makes one rotation in every 24 hours and completes a revolution about the sun in approximately 365.25 days. The earth revolves in an

elliptic orbit round the sun, with sun at one of the foci of the ellipse. The axis of the earth is inclined at an angle of 23.5° from the normal.

Fig. 2 Orbit of the earth around the sun

The distance between the sun and the earth varies by 1.7% due to the eccentricity of earth's orbit. 11 The mean earth-sun distance is 1.495 X 10 m and the sun subtends an angle of 32° on radiation outside the earth's atmosphere, results due to the radiation emitted by the sun and its spatial relationship to the earth. The energy from the sun received on a unit area of surface perpendicular to the propagation of radiation, per unit time, at the earth's mean distance from the sun outside the earth's atmosphere (extra terrestrial) is called Solar Constant. It is also referred to as extraterrestrial radiation. 2

The value of solar constant, ISC is now adopted as 1367 W//m .

Terrestrial Energy: The solar radiation, through atmosphere, reaching the earth's surface can be categorized as beam radiation and diffuse radiation. Solar radiation between wavelengths 0.10 and 100µm is referred to as thermal radiation and between 0.29-2.3 µm of the spectra is the visible range. While passing through the earth's atmosphere, the solar radiation is subjected to the mechanisms of  atmospheric absorption and scattering. A fraction of the radiation reaching earth's surface is reflected back into atmosphere and the rest is absorbed by the earth's surface. The earth reflects about 30% of all the incoming solar radiation back to extra terrestrial region through atmosphere. The reflected radiation is again subjected to atmospheric action, due to ozone, oxygen, nitrogen, carbon dioxide, carbon monoxide and water vapor. The air molecules, dust and water droplets

cause the scattering effect resulting in the decrease of radiation. This atmospheric attenuation is named as Airmass. Airmass may be defined as the ratio of the optical thickness of atmosphere through which beam radiation passes to the optical thickness if the sun were at zenith.

Terminology: Beam radiation, Ib: The beam radiation, also termed as direct radiation, is defined as the solar radiation propagating along the line joining the receiving surface and the sun. The beam radiation depends on the cloudiness and dustiness of the atmosphere. Diffuse radiation, I d: The diffuse radiation is defined as the solar radiation scattered by dust, molecules and aerosols and it does not have unique direction. The sum of beam and diffuse radiations is called total radiation, I of global radiation. The clearness index Kt may be defined as the ratio of radiation received on a horizontal surface in a period (usually one day) to the radiation that would have been received on a parallel extra terrestrial surface in the same period.

Irradiation G (W/m2): It is defined as the rate at which radiant energy is incident on a surface per unit area of the surface. The incident energy per unit area on a surface found by the integration of irradiance over a specified time, usually an hour or a day.

Meridian: Meridian is an imaginary great circle on the surface of the earth passing through the north and south poles at right angles to the equator. All points on the same meridian have the same longitude. The lines of longitude start at the prime meridian, in Greenwich, England.

Latitude Ø: The latitude of a location is the angle made by the radial line, joining the given location to the centre of the earth, with its projection on the equatorial plane. For northern hemisphere, the latitude is positive and negative for southern hemisphere.

Longitude Ψ : The longitude is an imaginary line that runs from the North Pole to the South Pole at right angles to the equator. The distance between lines of longitude is greater at the equator and smaller at the higher latitudes. Time zones are correlated to longitude. The sun traverses each degree of  longitude in 4 minutes.

Fig. 3 Zenith and solar altitude angles

Slope

ß:

The angle between the plane surface under consideration and the horizontal is the slope. It is considered as positive for surface sloping towards south in northern hemisphere and vice versa. The various angles involved in the estimation of solar energy radiation are shown in the above figures.

Zenith angle θZ : The angle between sun's rays and a perpendicular line to the horizontal plane is known as zenith angle.

Solar altitude angle α: It is defined as the angle between the sunrays and its projection on a horizontal plane It is complementary to the zenith angle. α+ θZ =90 °

Surface azimuth angle γ: It is the angle in the horizontal plane between the line due south and the projection of the normal to the inclined surface on the horizontal plane. It is considered positive if the projection is east of  south and negative if the projection is west of northern hemisphere.

Solar azimuth angle γs: It is the angle in a horizontal plane between the line due south and the projection of beam radiation on the horizontal plane. For northern hemisphere, depending upon whether the projection is east of south or west of south, the angle is taken as positive or negative respectively. The case is vice versa for southern hemisphere.

Local apparent time or Solar time LAT: It is the time evaluated based on the apparent angular motion of the sun, with solar noon denoting the time. The sun crosses the meridian of the observer.

Standard Time ST: It is the civil time that is followed based on a standard meridian in a time zone. A region spread over 15 ° of longitude has a common time zone. The sun traverses each degree of longitude in 4 minutes. The standard meridian ?STD for the Indian time zone is 82° 44' E and the solar time based on this standard meridian is the Indian Standard Time IST.  LAT = IST -4 (ψSTD - ψL) + E 

Where ψL is the longitude of the location expressed in degrees. The equation of time E is the correction compensating for the variation in the length of the day which is not exactly 24 hours. This correction in time which is not greater than ±15 minutes can be evaluated for any day of the year using the expression E = 9.87 sin2B - 7.53 cosB - 1.5 sinB B = (n-81) X 360/364, the value of n varies from 1 to 365.

Declination δ: It is defined as the angle between the line joining the centers of the sun and the earth and its projection on the equatorial plane. This declination is the result of the rotation of the earth about an axis making an angle of 661/2° with the plane of its rotation around the sun. The declination varies from a maximum value of +23.45° on June 21 to a minimum value of -23.45° on December 21. The declination can be calculated with the following equation: δ = 23.45 sin [360(284+n)/65] s

st

where n is the day of the year. January 1 t is taken as 1 and n for February 1 is 32 and so on.

Fig. 5 Declination and hour angle

Hour angle ω: It may be defined as the angle through which the earth must be rotated to bring the meridian of  the plane directly in line with the sun, it is the angular displacement of the sun east or west of the local meridian, due to the rotation of earth on its axis at 15° per hour (360° / 24hr = 15° / hr). The hour angle is zero at solar noon, positive in the morning and negative in the afternoon. It can be evaluated using: ω = 15 (12:00 - LAT) where LAT is the local apparent time or local solar time in hours.

Solar radiation measurements The instruments for measuring solar radiation can be classified into two categories, namely Pyrheliometer and Pyranometer. Pyrheliometer: This is an instrument using a collimated detector for measuring solar radiation from the sun and from a small portion of the sky around the sun (i.e. beam radiation) at normal incidence.

Fig. 6 Pyrheliometer Working principle: Two blackened manganin strips are used which are arranged in such a way that either of them are exposed to radiation at the base of collimating tubes by operating a reversible shutter. Each strip can be electrically heated and there is a thermocouple provided. When one strip is exposed to radiation, the other strip is shaded and a current is passed through the shaded strip to heat it to the same temperature as the exposed strip. Since the temperature difference is zero, the electrical energy to the shaded strip should be equal to the solar radiation absorbed by the exposed strip. The electrical energy produced is equated to the product of solar radiation, strip area and absorptance. Hence, solar energy is determined. Then the shutter's position is reversed, thereby interchanging the radiation and electric heating and the second value is determined. The edge effects of the strips and non-uniform electrical heating, which results in minor differences in the functioning of the strips, are compensated by the above mentioned interchange. The detectors do not distinguish between scattered radiation and beam radiation. Thin clouds or haze can affect the angular distribution of radiation within the field of view of standard Pyrheliometer.

Fig. 7 Circuit diagram of Pyrheliometer

Pyranometer: This instrument is used for measuring the total radiation (beam + diffuse), usually incident on the surface. It can be used to measure diffuse radiation only by using a shade ring or disc, which shades the beam radiation.

Fig. 8 Pyranometer This instrument is used to measure global radiation on a horizontal surface. It works on identical principle of that of Pyrheliometer except that the sensitive surface is exposed to total radiation. i.e., inclusive of beam, diffuse and reflected from earth and surroundings. The sensitive surface comprises of a circular blackened multi junctions thermopile. The hot and cold junctions are electrically insulated from the basement. The radiation incident on the surface results in a temperature difference between hot and cold  junctions. Two concentric hemispherical glass domed covers the sensitive surface thereby

shielding it from wind and rain and to reduce convection currents. The beam radiation can be blocked by an occulting disc provided to facilitate measurement of diffuse radiation. The Pyranometer is calibrated to measure solar radiation on a horizontal surface. Hence, when the surface is tilted the changes of the regime of free convection within glass dome may result in erroneous measurement. Hence, care should be taken to locate the Pyranometer always horizontally. The thermopile detectors used in Pyranometer and Pyrheliometer convert the incident solar radiation into mill volts. Hence a potentiometer is required to detect and record this output.

Sunshine recorder: This instrument is used to measure the duration, in hours of bright sunshine during the course of  the day. A glass sphere is mounted in a section of spherical bowl with grooves for holding the recorder cards. When exposed to sun, the sphere burns a trace on the card; the length of the brace is a direct measure of the duration of bright sunshine. There are sets of grooves on the card for summer and winter.

Fig. 11Sunshine recorder (Courtesy: Campbell scientific Inc.)

Flux falling on horizontal and inclined surfaces If  θ  is the angle between an incident beam of flux Ib and the normal to a plane surface, the equivalent flux falling normal to the surface is given as I bcosθ . Before a solar energy collector is installed, it is essential to know the availability of collectable solar energy. Based on this data and the projected pattern of energy usage from the device, the size of the collector can be estimated. This required data would be of several years of  measurements of irradiance on the proposed collector plane. The statistical measures required have to be estimated from available statistical data or from nearby site appearing to have several irradiance. Past irradiance can be used to predict future irradiance. The design methods usually relay on approximate averages, such as monthly means of daily insolation (irradiation).