Solar radiation, often referred to as insolation, is the electromagnetic energy emitted by the sun that reaches the Earth. Calculating this energy at a specific location on the surface is foundational for many applications, including planning solar energy systems, optimizing crop growth, and developing accurate climate models. The calculation process involves determining the theoretical maximum energy outside the atmosphere and then accounting for factors that reduce that energy before it hits the ground.
Fundamental Variables Required
The calculation begins by establishing the precise geometric relationship between the sun and the receiving surface. Location is defined using latitude and longitude, which determines the sun’s maximum height in the sky throughout the year.
The time of day and the time of year must be accurately determined using solar time. The day of the year is used to calculate the sun’s declination angle, which is the angular position of the sun relative to the Earth’s equator. This angle accounts for the seasonal variation in solar energy.
The solar zenith angle is the angle between the sun’s rays and a vertical line pointing straight up from the ground. This angle dictates the intensity of the solar beam hitting a horizontal surface. For tilted surfaces, two additional variables are needed: the surface tilt angle (inclination from the horizontal) and the surface azimuth angle (compass direction the surface faces). These variables define the angle of incidence between the sun’s rays and the line perpendicular to the surface.
Calculating Extraterrestrial Radiation
The theoretical maximum energy available must be established by calculating the extraterrestrial radiation, the amount of solar energy received on a surface outside the Earth’s atmosphere. This calculation starts with the solar constant, the average rate at which solar energy reaches the top of the atmosphere on a plane perpendicular to the sun’s rays.
The accepted value for the solar constant is approximately \(1,367 \text{ W/m}^2\). This value is not truly constant because the Earth’s elliptical orbit causes the distance between the Earth and the sun to change throughout the year. This variation causes the extraterrestrial radiation to fluctuate by about \(\pm 3.3\%\) annually.
The calculation adjusts the solar constant based on the Earth-Sun distance, determined by the day of the year using a correction factor derived from the inverse square law of radiation. When the Earth is closest to the sun (perihelion) in early January, the radiation is at its peak. When the Earth is farthest (aphelion) in early July, the energy is at its minimum.
Accounting for Atmospheric Effects
The theoretical extraterrestrial radiation must be reduced to find the actual energy reaching the surface, as the atmosphere acts as a complex filter. The primary processes responsible for this reduction are absorption and scattering, collectively called attenuation. Gases like ozone absorb most of the high-energy ultraviolet radiation, while water vapor and carbon dioxide absorb energy in specific infrared wavelengths.
Absorption and Scattering
Scattering occurs when solar radiation interacts with air molecules and suspended particles like dust and aerosols. Rayleigh scattering, caused by air molecules, preferentially scatters shorter-wavelength blue light, which is why the sky appears blue. Mie scattering, caused by larger particles, scatters light more uniformly.
The amount of atmosphere the sun’s rays must pass through is quantified by the Air Mass value. Air Mass is defined as the ratio of the actual path length of the solar beam through the atmosphere to the shortest possible path length, which occurs when the sun is directly overhead. As the sun moves lower towards the horizon, the path length increases, leading to a higher Air Mass value and a greater loss of energy through both absorption and scattering.
Irradiance Components
The energy that reaches the ground is categorized into three main components:
- Direct Normal Irradiance (DNI) is the solar radiation that travels in a straight line from the sun and casts a sharp shadow.
- Diffuse Horizontal Irradiance (DHI) is the radiation that has been scattered by the atmosphere and clouds, arriving at the surface from all directions.
- Global Horizontal Irradiance (GHI) is the total solar radiation incident on a horizontal surface, calculated as the sum of DNI and DHI.
To perform accurate calculations, especially for clear-sky conditions, specialized atmospheric models are employed. Simple models, such as the Bird or Hottel clear-sky models, use empirical equations to estimate atmospheric transmittance based on factors like water vapor content and aerosol optical depth. More sophisticated models, like the Perez model, are required to accurately separate the total radiation into its DNI and DHI components, which is necessary for calculating the energy received on a tilted surface.
Practical Tools and Real-World Data
While the underlying physics is complex, most modern calculations of surface solar radiation rely on historical measurements and sophisticated data tools rather than manual calculations. These tools utilize the geometric and atmospheric principles but apply them across vast datasets. The most accurate data comes from ground-based measurements using instruments like pyranometers (which measure GHI) and pyrheliometers (which measure DNI).
Since ground measurement stations are sparse, models are used to fill the gaps, often relying on satellite imagery and atmospheric data. Large-scale, publicly accessible online databases provide this modeled and measured data for virtually any location on Earth. Examples include the National Solar Radiation Database (NSRDB) for the United States and the Global Solar Atlas, which provides global coverage.
These online tools allow a user to input a location and quickly retrieve long-term average solar radiation data, often broken down into GHI, DNI, and DHI components. Specialized solar modeling software integrates these data sources with geometric equations to predict the energy yield for a specific system, such as a solar farm, taking into account its tilt and orientation.