2.1 Available Solar Radiation and How It Is Measured

2.1 Available Solar Radiation and How It Is Measured

Before talking about concentration of light for practical purposes, it would be good for us to review what kinds of natural radiation are available to us and how that radiation is characterized and measured.

Solar Constant

The fraction of the energy flux emitted by the sun and intercepted by the earth is characterized by the solar constant. The solar constant is defined as essentially the measure of the solar energy flux density perpendicular to the ray direction per unit area per unit of time. It is most precisely measured by satellites outside the earth atmosphere. The solar constant is currently estimated at 1361 W/m² [cited from Kopp and Lean, 2011]. This number actually varies by 3% because the orbit of the earth is elliptical, and the distance from the sun varies over the course of the year. Some small variation of the solar constant is also possible due to changes in Sun's luminosity. This measured value includes all types of radiation, a substantial fraction of which is lost as the light passes through the atmosphere [IPS - Radio and Space Services].

Transformations in the Atmosphere

As the solar radiation passes through the atmosphere, it gets absorbed, scattered, reflected, or transmitted. All these processes result in reduction of the energy flux density. Actually, the solar flux density is reduced by about 30% compared to extraterrestrial radiation flux on a sunny day and is reduced by as much as 90% on a cloudy day. The following main losses should be noted:

• absorbed by particles and molecules in the atmosphere - 10-30%
• reflected and scattered back to space - 2-11%
• scattered to earth (direct radiation becomes diffuse) - 5-26% [Stine and Harrigan, 1986]

As a result, the direct radiation reaching the earth surface (or a device installed on the earth surface) never exceeds 83% of the original extraterrestrial energy flux. This radiation that comes directly from the solar disk is defined as beam radiation. The scattered and reflected radiation that is sent to the earth surface from all directions (reflected from other bodies, molecules, particles, droplets, etc.) is defined as diffuse radiation. The sum of the beam and diffuse components is defined as total (or global) radiation.

It is important for us to differentiate between the beam radiation and diffuse radiation when talking about solar concentration in this lesson, because the beam radiation can be concentrated, while the diffuse radiation, in many cases, cannot. For that matter, the solar systems utilizing concentrating collectors will work best in sunny locations and may be not feasible in those with a lot of weather variability and clouds. 

Solar Radiation Metrics

Consider the following metrics commonly used to report the solar resource (irradiance) data. These values can be determined from the field measurements or from empirical correlations.  

Theoretically, these three metrics are interrelated:

However, in practice, field measurements may somewhat deviate from this relationship.

A typical solar resource data file (Typical Meteorological Year or TMY) would include all of these metrics measured for a specific location for each hour for each day in a year. Note that these values (measured in W/m²) indicate the instantaneous solar flux, which of course will vary during the day. In the morning and in the evening, the irradiance will be lower, but it will often reach its peak around solar noon. If there are clouds or other weather phenomena, the irradiance will temporarily drop.

The plots below give you an example of such variance. The GHI, DNI, and DHI data are plotted for the day of March 21st (equinox) in Orlando, FL. While it seemed to be a relatively sunny day (the beam component evidently dominates over diffuse, reaching ~900 W/m²), there are some minor interruptions (possibly from clouds) to this profile.

Daily profiles for different types of solar radiation in Orlando, FL, on March 21 - extracted from the TMY weather file. 

Credit: Mark Fedkin

The TMY files with all these metrics given for each day for different locations around the globe are publicly available from the NSRDB database. 

Solar Maps

The GHI data are also used to generate solar resource maps. However, the instantaneous values of global irradiance are not best for mapping due to their continuous variability. Instead, GHI are integrated to determine the daily average irradiation (total energy from the sky).

Look again at the GHI plot (blue curve above) – essentially, this total daily energy will be equal to the area under the irradiance curve! This total daily irradiation value (measured in kWh/m²/day) can be better related to the total energy converted and delivered by your solar system. In a practical sense, it is a more intuitive metric to map.

Also, let’s not forget the seasonal variations. The solar daily irradiation will be understandably higher during summer months and lower during winter months. Hence, the map below is based on the annual average values of daily irradiation.

Solar Irradiation Map for the U.S. in terms of annual average daily GHI (kWh/m²/day)

Sengupta, M., Y. Xie, A. Lopez, A. Habte, G. Maclaurin, and J. Shelby. 2018. "The National Solar Radiation Data Base (NSRDB)." Renewable and Sustainable Energy Reviews 89 (June): 51-60.

National Renewable Energy Laboratory

Short-Wave and Long-Wave

Short-wave radiation, in the wavelength range from 0.3 to 3 μm, comes directly from the sun. It includes both beam and diffuse components.

Long-wave radiation, with wavelength 3 μm or longer, originates from the sources at near-ambient temperatures - atmosphere, earth surface, light collectors, other bodies.

The solar radiation reaching the earth is highly variable and depends on the state of the atmosphere at a specific locale. Two atmospheric processes can significantly affect the incident irradiation: scattering and absorption.

Scattering is caused by interaction of the radiation with molecules, water, and dust particles in the air. How much light is scattered depends on the number of particles in the atmosphere, particle size, and the total air mass the radiation comes through.

Absorption occurs upon interaction of the radiation with certain molecules, such as ozone (absorption of short-wave radiation - ultraviolet), water vapor, and carbon dioxide (absorption of long-wave radiation - infrared).

Due to these processes, out of the whole spectrum of solar radiation, only a small portion reaches the earth's surface. Thus, most x-rays and other short-wave radiation is absorbed by atmospheric components in the ionosphere, ultraviolet is absorbed by ozone, and not-so abundant long-wave radiation is absorbed by CO2. As a result, the main wavelength range to be considered for solar applications is from 0.29 to 2.5 μm  [Duffie and Beckman, 2013].

Figure 2.1. Different types of radiation at the earth surface: orange - short wave; blue - long wave.

Credit: Mark Fedkin - modified after Duffie and Beckman, 2013

Transmittance

The effects of radiation scattering and absorption vary with the time of the day (due to the change of the air mass through which the beam passes through) and seasonally with the time of the year. Hence, the actual beam irradiance on the surface can be empirically estimated using a set of atmospheric parameters and Sun-Earth geometry.

Hottel’s method (Hottel 1976) describes the beam radiation transmitted through the atmosphere under the “clear-sky” conditions using atmospheric transmittance coefficient.

$$G_{bn}={\tau }_b\times G_{on}$$

where G _bn is the beam irradiance normal to the receiving surface, G _on is the extraterrestrial irradiance (solar constant in a general case), and τ _b is beam transmittance.

The transmittance value can be evaluated by Hottel’s model using solar zenith angle and altitude for several different climate regimes. Or, it can be determined by direct measurement of the beam irradiance on the normal surface.

Instruments

The amount of solar radiation on the earth's surface can be instrumentally measured, and precise measurements are important for providing background solar data for solar energy conversion applications.

Described below are the most important types of instruments to measure solar radiation:

1. Pyrheliometer is used to measure direct beam radiation at normal incidence. There are different types of pyrheliometers. According to Duffie and Beckman (2013), Abbot silver disc pyrheliometer and Angstrom compensation pyrheliometer are important primary standard instruments. Eppley normal incidence pyrheliometer (NIP) is a common instrument used for practical measurements in the US, and Kipp and Zonen actinometer is widely used in Europe. Both of these instruments are calibrated against the primary standard methods.

   Based on their design, the above listed instruments measure the beam radiation coming from the sun and a small portion of the sky around the sun. Based on the experimental studies involving various pyrheliometer design, the contribution of the circumsolar sky to the beam is relatively negligible on a sunny day with clear skies. However, a hazy sky or a uniform thin cloud cover redistributes the radiation so that the contribution of the circumsolar sky to the measurement may become more significant.

2. Pyranometer is used to measure total hemispherical radiation - beam plus diffuse - on a horizontal surface. If shaded, a pyranometer measures diffuse radiation. Most of solar resource data come from pyranometers. The total irradiance (W/m²) measured on a horizontal surface by a pyranometer is expressed as follows:

   \[{I_{tot}} = {I_{beam}}\cos \theta + {I_{diff}}\]

   (2.1)

   where θ is the zenith angle (i.e., angle between the incident ray and the normal to the horizontal instrument plane.

   Examples of pyranometers are Eppley 180^o or Eppley black-and-white pyranometers in the US and Moll-Gorczynsky pyranometer in Europe. These instruments are usually calibrated against standard pyrheliometers. There are pyranometers with thermocouple detectors and with photovoltaic detectors. The detectors ideally should be independent on the wavelength of the solar spectrum and angle of incidence. Pyranometers are also used to measure solar radiation on inclined surfaces, which is important for estimating input to collectors. Calibration of pyranometers depends on the inclination angle, so experimental data are needed to interpret the measurements.

3. Photoelectric sunshine recorder. The natural solar radiation is notoriously intermittent and varying in intensity. The most potent radiation that creates the highest potential for concentration and conversion is the bright sunshine, which has a large beam component. The duration of the bright sunshine at a locale is measured, for example, by a photoelectric sunshine recorder. The device has two selenium photovoltaic cells, one of which is shaded, and the other is exposed to the available solar radiation. When there is no beam radiation, the signal output from both cells is similar, while in bright sunshine, signal difference between the two cells is maximized. This technique can be used to monitor the bright sunshine hours.

   A more detailed explanation of how these instruments work and what kind of data is obtained from those measurements is available in the following Duffie and Beckman (2013) book, referred below. Please spend some time acquiring basic knowledge on solar resource data. For everyone who took EME 810 and is more or less familiar with this topic, this still may be a useful refresher.

Solar radiation data collected through the above-mentioned instrumental methods provide the basis for development of any solar projects. We can summarize the types of solar resource data as follows:

Figure 2.2. Overview of different types of solar radiation data.

Click here for a text description

Solar radiation data supplied via pyrheliometric and pyranometric measurements may represent time resolved information: e.g., irradiance (instantaneous measurements of solar energy flux), irradiation (integrated energy flux over time), or averaged irradiation. Depending on measurement setup, the data can be for horizontal or inclined surface. The data can characterize different types of radiation: beam, diffuse, or total.

Credit: Mark Fedkin

Before moving on, please work through the following self-check questions to assess your learning: