While the solar radiation incident on the Earth's atmosphere is relatively constant, the radiation at the Earth's surface varies widely due to:
- atmospheric effects, including absorption and scattering;
- local variations in the atmosphere, such as water vapour, clouds, and pollution;
- latitude of the location; and
- the season of the year and the time of day.
The above effects have several impacts on the solar radiation received at the Earth's surface. These changes include variations in the overall power received, the spectral content of the light and the angle from which light is incident on a surface. In addition, a key change is that the variability of the solar radiation at a particular location increases dramatically. The variability is due to both local effects such as clouds and seasonal variations, as well as other effects such as the length of the day at a particular latitude. Desert regions tend to have lower variations due to local atmospheric phenomena such as clouds. Equatorial regions have low variability between seasons.
These false-color images show the average solar insolation, or rate of incoming sunlight at the Earth's surface, over the entire globe for the months of January and April. The colors correspond to values (kilowatt hours per square meter per day) measured every day by a variety of Earth-observing satellites and integrated by the International Satellite Cloud Climatology Project (ISCCP). NASA's Surface Meteorology and Solar Energy (SSE) Project compiled these data--collected from July 1983 to June 1993--into a 10-year average for that period.
From this data it is self-evident that South Africa should be doing a lot more to harvest the abundance of solar energy that the country receives throughout the year.
Atmospheric effects have several impacts on the solar radiation at the Earth's surface. The major effects for photovoltaic applications are:
- a reduction in the power of the solar radiation due to absorption, scattering and reflection in the atmosphere;
- a change in the spectral content of the solar radiation due to greater absorption or scattering of some wavelengths;
- the introduction of a diffuse or indirect component into the solar radiation; and
- local variations in the atmosphere (such as water vapour, clouds and pollution) which have additional effects on the incident power, spectrum and directionality.
Absorption in the Atmosphere
As solar radiation passes through the atmosphere, gasses, dust and aerosols absorb the incident photons. Specific gasses, notably ozone (O3), carbon dioxide (CO2), and water vapour (H2O), have very high absorption of photons that have energies close to the bond energies of these atmospheric gases. This absorption yields deep troughs in the spectral radiation curve. For example, much of the far infrared light above 2 µm is absorbed by water vapour and carbon dioxide. Similarly, most of the ultraviolet light below 0.3 µm is absorbed by ozone (but not enough to completely prevent sunburn!).
While the absorption by specific gasses in the atmosphere change the spectral content of the terrestrial solar radiation, they have a relatively minor impact on the overall power. Instead, the major factor reducing the power from solar radiation is the absorption and scattering of light due to air molecules and dust. This absorption process does not produce the deep troughs in the spectral irradiance, but rather causes a power reduction dependant on the path length through the atmosphere. When the sun is overhead, the absorption due to these atmospheric elements causes a relatively uniform reduction across the visible spectrum, so the incident light appears white. However, for longer path lengths, higher energy (lower wavelength) light is more effectively absorbed and scattered. Hence in the morning and evening the sun appears much redder and has a lower intensity than in the middle of the day.
Direct and Diffuse Radiation Due to Scattering of Incident Light
Light is absorbed as it passes through the atmosphere and at the same time it is subject to scattering. One of the mechanisms for light scattering in the atmosphere is known as Rayleigh scattering which is caused by molecules in the atmosphere. Rayleigh scattering is particularly effective for short wavelength light (that is blue light) since it has a λ-4 dependence. In addition to Rayleigh scattering, aerosols and dust particles contribute to the scattering of incident light known as Mie scattering.
Scattered light is undirected, and so it appears to be coming from any region of the sky. This light is called "diffuse" light. Since diffuse light is primarily "blue" light, the light that comes from regions of the sky other than where the sun is, appears blue. In the absence of scattering in the atmosphere, the sky would appear black, and the sun would appear as a disk light source. On a clear day, about 10% of the total incident solar radiation is diffuse.
Effect of clouds and other local variations in the atmosphere
The final effect of the atmosphere on incident solar radiation is due to local variations in the atmosphere. Depending on the type of cloud cover, the incident power is severely reduced. An example of heavy cloud cover is shown below.
The Air Mass is the path length which light takes through the atmosphere normalized to the shortest possible path length (that is, when the sun is directly overhead). The Air Mass quantifies the reduction in the power of light as it passes through the atmosphere and is absorbed by air and dust. The Air Mass is defined as:
where θ is the angle from the vertical (zenith angle). When the sun is directly overhead, the Air Mass is 1.
The above calculation for air mass assumes that the atmosphere is a flat horizontal layer, but because of the curvature of the atmosphere, the air mass is not quite equal to the atmospheric path length when the sun is close to the horizon. At sunrise, the angle of the sun from the vertical position is 90° and the air mass is infinite, whereas the path length clearly is not. An equation which incorporates the curvature of the earth is:
Standardised Solar Spectrum and Solar Irradiation
The efficiency of a solar cell is sensitive to variations in both the power and the spectrum of the incident light. To facilitate an accurate comparison between solar cells measured at different times and locations, a standard spectrum and power density has been defined for both radiation outside the Earth's atmosphere and at the Earth's surface.
The standard spectrum at the Earth's surface is called AM1.5G, (the G stands for global and includes both direct and diffuse radiation) or AM1.5D (which includes direct radiation only). The intensity of AM1.5D radiation can be approximated by reducing the AM0 spectrum by 28% (18% due to absorption and 10% to scattering). The global spectrum is 10% higher than the direct spectrum. These calculations give approximately 970 W/m2 for AM1.5G. However, the standard AM1.5G spectrum has been normalized to give 1kW/m2 due to the convenience of the round number and the fact that there are inherently variations in incident solar radiation.
The standard spectrum outside the Earth's atmosphere is called AM0, because at no stage does the light pass through the atmosphere. This spectrum is typically used to predict the expected performance of cells in space.
Intensity Calculations Based on the Air Mass
The intensity of the direct component of sunlight throughout each day can be determined as a function of air mass from the experimentally determined equation :
where ID is the intensity on a plane perpendicular to the sun's rays in units of kW/m2 and AM is the air mass. The value of 1.353 kW/m2 is the solar constant and the number 0.7 arises from the fact that about 70% of the radiation incident on the atmosphere is transmitted to the Earth. The extra power term of 0.678 is an empirical fit to the observed data and takes into account the non-uniformities in the atmospheric layers.
Sunlight intensity increases with the height above sea level. The spectral content of sunlight also changes making the sky 'bluer' on high mountains. Much of the southwest of the United States is two kilometers above sea level, adding significantly to solar isolation. A simple empirical fit to observed data and accurate to a few kilometers above sea level is given by:
where a = 0.14 and h is the location height above sea level in kilometers.
Even on a clear day, the diffuse radiation is still about 10% of the direct component. Thus on a clear day the global irradiance on a module perpendicular to the sun's rays is:
Arbitrary Orientation and Tilt
For a module at an arbitrary tilt and orientation the equation becomes a little more complicated:
α is the sun elevation angle and Θ is the sun azimuth angle. β is the module tilt angle. A module lying flat on the ground has β =0° and a vertical module has a β =90°. Φ is the azimuth angle that the module faces. The vast majority of modules are aligned to face towards the equator. A module in the southern hemisphere will be facing north with Ψ = 0° and a module in the northern hemisphere will typically face directly south with Ψ = 180°. Smodule and Sincident are respectively the light intensities on the module and of the incoming light in W/mē, the Sincident being a direct only component.
A module that directly faces the sun so that the incoming rays are perpendicular to the module surface has the module tilt equal to the sun's zenith angle (90 - α = β), and the module azimuth angle equal to the sun's azimuth angle (Φ = Θ).
The following calculations combine the calculation of sun's position with the Airmass formula and then calculates the intensity of light incident on a module with arbitrary tilt and orientation.
Measurement of Solar Radiation
In PV system design it is essential to know the amount of sunlight available at a particular location at a given time. The two common methods which characterise solar radiation are the solar radiance (or radiation) and solar insolation. The solar radiance is an instantaneous power density in units of kW/m2. The solar radiance varies throughout the day from 0 kW/m2 at night to a maximum of about 1 kW/m2. The solar radiance is strongly dependant on location and local weather. Solar radiance measurements consist of global and/or direct radiation measurements taken periodically throughout the day. The measurements are taken using either a pyranometer (measuring global radiation) and/or a pyrheliometer (measuring direct radiation). In well established locations, this data has been collected for more than twenty years.
An alternative method of measuring solar radiation, which is less accurate but also less expensive, is using a sunshine recorder. These sunshine recorders (also known as Campbell-Stokes recorders), measure the number of hours in the day during which the sunshine is above a certain level (typically 200 mW/cm2). Data collected in this way can be used to determine the solar insolation by comparing the measured number of sunshine hours to those based on calculations and including several correction factors.
A final method to estimate solar insolation is cloud cover data taken from existing satellite images.
While solar irradiance is most commonly measured, a more common form of radiation data used in system design is the solar insolation. The solar insolation is the total amount of solar energy received at a particular location during a specified time period, often in units of kWh/(m2 day). While the units of solar insolation and solar irradiance are both a power density (for solar insolation the "hours" in the numerator are a time measurement as is the "day" in the denominator), solar insolation is quite different than the solar irradiance as the solar insolation is the instantaneous solar irradiance averaged over a given time period. Solar insolation data is commonly used for simple PV system design while solar radiance is used in more complicated PV system performance which calculates the system performance at each point in the day. Solar insolation can also be expressed in units of MJ/m2 per year
Solar radiation for a particular location can be given in several ways including:
- Typical mean year data for a particular location
- Average daily, monthly or yearly solar insolation for a given location
- Global isoflux contours either for a full year, a quarter year or a particular month
- Sunshine hours data
- Solar Insolation Based on Satellite Cloud-Cover Data
- Calculations of Solar Radiation