Direct insolation

Direct insolation, also known as direct normal irradiance, or its acronym, DNI, is the insolation measured at a given location on Earth with a surface element perpendicular to the Sun's rays, excluding diffuse insolation (the solar radiation that is scattered or reflected by atmospheric components in the sky). Direct insolation is equal to the solar irradiance above the atmosphere minus the atmospheric losses due to absorption and scattering. While the solar irradiance above the atmosphere varies with the Earth–Sun distance and solar cycles, the losses depend on the time of day (length of light's path through the atmosphere depending on the solar elevation angle), cloud cover, humidity, and other impurities.

Simplified formula

A simple formula gives the approximate level of direct insolation when there are no clouds:^[1]

$${\displaystyle I_{D}=1.353{\text{ kW/m}}^{2}\times 0.7^{AM^{0.678}}}$$

where AM is the airmass given, approximately, by

$${\displaystyle AM={\frac {1}{\cos \theta }}}$$

with θ being the solar zenith angle (90° minus the altitude) of the sun. While the above formula for airmass gives reasonable results for solar zenith angles up to 60°, it degrades rapidly afterwards, especially after 75°. For more accurate formulas, refer to the main article about airmass.

For the sun at the zenith, this gives 947 W/m². However, another source states that direct sunlight under these conditions, with 1367 W/m² above the atmosphere, is about 1050 W/m², and total insolation about 1120 W/m².^[2]

Average direct insolation

For practical purposes, a time-average of the direct insolation over the course of the year is commonly used. This averaging takes into account the absence of sunlight during the night, increased scatter in the morning and evening hours, average effects of cloud cover and smog, as well as seasonal variations of the mid-day solar elevation.

Units of measurement

Direct insolation is measured in watts per square metre (W/m²) or kilowatt-hours per square meter per day (kW·h/(m²·day)).

1 kW·h/(m²·day) = 1,000 W · 1 hour / ( 1 m² · 24 hours) = 41.67 W/m²

In the case of photovoltaics, average direct insolation is commonly measured in terms of peak direct insolation as kWh/(kWp·y) (kilowatt hours per year per kilowatt peak rating).

Applications

Since radiation directly from the sun can be focussed with mirrors and lens, it can be applied to concentrated solar thermal (CST) systems.^[3][4][5] Due to clouds and aerosols, the direct insolation can fluctuate throughout the day, so forecasting the available resource is important in these applications ^[6][7]

Not to be confused with DirHI

It is usually assumed that the term direct irradiance, direct radiation, or direct insolation refers to the irradiance intercepted by a surface normal, or perpendicular, to the direct sunlight. However, when the word normal is omitted, it can also mean direct horizontal irradiance (DirHI), the direct irradiance received on a horizontal surface^[8]. The following relation holds $${\displaystyle {\text{DirHI}}={\text{DNI}}\times \cos(z)}$$ for instantaneous and coincident values of DirHI, DNI and ${\displaystyle z}$, the solar zenith angle. For means of DirHI, DNI and ${\displaystyle z}$ over finite periods of time from minutes up to an hour, the above relation may be used approximately.

See also

• Solar irradiance- main article discussing total solar irradiance and subcomponents direct normal, diffuse horizontal, global horizontal, global tilted and global normal irradiances.
• Diffuse sky radiation