Irradiance sensors are often used in calculating energy balances. When calculating net radiation, irradiance measurements form the main components for your calculation. Therefore, accurate measurements are essential for composing a correct energy balance. This article will guide you through the components used in an energy balance and offer some tips on how to keep your calculations reliable.

What is an energy balance?

When calculating an energy balance, we are interested in the net radiation, or net flux, available to influence the climate. This is the balance between the incoming and outgoing energy at the ground surface of the earth. In the case of a solar energy balance, information about how much radiation from the sun is absorbed by a surface or object is required. With the right irradiance sensors, the radiation components that make up the energy balance can be measured. For more information on how to take accurate solar measurements, read our article on how to get the best solar radiation measurements. The calculation of net radiation requires four components: global solar radiation, for example solar radiation, downward longwave radiation, and upward longwave radiation.

Main elements when you calculate solar energy

A total energy balance consists of four main components: global solar radiation (Eg↓), downward longwave radiation (El↓), reflected solar radiation (Er↑), and upward longwave radiation (El↑).

Global solar radiation (Eg↓)

The sun emits a broad spectrum of wavelengths, including visible light, allowing us to see in daylight. Visible light has a short wavelength compared to radiation from heat. Therefore, visible light is part of the shortwave radiation spectrum. Measuring solar irradiance can be done with a pyranometer. A pyranometer measures radiation primarily in the range of ultraviolet (UV), visible, and near-infrared (NIR) regions of the spectrum. This combined range corresponds to 285 to 3000 nm.

To measure shortwave radiation, our pyranometers are equipped with a glass dome that only transmits shortwave radiation. Underneath the dome, a black-coated thermopile detector is located. The transmitted shortwave radiation heats the black coating and causes a temperature difference over the thermopile. A thermopile detector converts thermal energy into electrical energy. This allows a pyranometer to measure the transmitted shortwave radiation.

Reflected solar radiation (Er↑)

Not all global solar radiation is absorbed by the earth’s surface. When radiation emitted by the sun reaches a surface, part of it is absorbed, part is transmitted, and part is reflected into the atmosphere. Depending on the surface reflectance (albedo) of the surface, a significant part of the incoming radiation is reflected. Snow, for example, reflects a lot of sunlight, whereas asphalt does not.

Snow reflects a large part of the sunlight

Figure 1 Snow reflects a large part of the sunlight.
To measure the reflected solar radiation, a downward-facing pyranometer is required. When calculating an energy balance, we are interested in the net radiation absorbed by a surface. The reflected radiation is not being absorbed by a surface; thus, this component should be subtracted from the total incoming radiation.

Asphalt absorbs most of the light

Figure 2 Asphalt absorbs most of the light.

Downward longwave radiation (El↓)

Besides visible light, the sun also emits radiation outside of the visible range with longer wavelengths. We call this longwave radiation, which falls within the infrared spectrum and ranges from 3000 nm onwards. We feel this longwave radiation as heat.

In the longwave spectrum, the sky can be seen as a temperature source, colder than ground-level ambient air temperature. Here, the lowest temperature is in the direction perpendicular to the surface and gets warmer (closer to ambient air temperature) at the horizon. When measuring downward longwave radiation, the sky can be seen as a blackbody, which comes with an “equivalent blackbody” temperature. The uniformity of the longwave source is much better than that of radiation in the solar spectrum and thus is less affected by weather conditions. The thermal radiation emitted by a blackbody can be determined using the Stefan-Boltzmann law:

El = σ·(T + 273,15)4

Where:

El = longwave radiation [W/m2]

σ = Stefan-Boltzmann constant [5.67 × 10-8 W·m-2·K-4] 

T = temperature of the measured surface [°C]  

To measure only longwave radiation without including shortwave radiation, a pyrgeometer can be used. A pyrgeometer, just like a pyranometer, is built with a black-coated thermopile detector located underneath a dome. However, this dome is made of silicon with a solar blind filter that transmits longwave radiation and blocks shortwave radiation. This allows for performing measurements with solely longwave radiation without being affected by shortwave radiation. Since water blocks longwave radiation, pyrgeometers often have heaters to improve the reliability of the measurements.

Because the pyrgeometer itself has a temperature above absolute zero, it also emits longwave radiation. This must be considered when calculating the net radiation. To compensate for this, a Pt100 temperature sensor is included in the instrument body. This allows us to determine its own emission and subtract this from the total measured emission.

Upward longwave radiation (El↑)

Longwave radiation does not just originate from the sky. Every object with a temperature higher than absolute zero emits longwave radiation, including the earth itself. How much an object emits also depends on its emissivity. However, when calculating the net radiation, we use an object’s equivalent to blackbody radiative temperature. This means we assume the source has an emission coefficient of 1 which means it does not reflect any light. This allows us to determine the temperature of the surface of the earth using the Stefan-Boltzmann law.

Unlike solar radiation, longwave radiation is barely reflected by the surface of the earth, and therefore, we neglect longwave radiation when calculating the net radiation.

Final energy balance

Adding all the elements in the right way, we end up with the final equation for calculating the net radiation:

E* = E↓ - E↑ = Eg↓ + El↓ - Er↑ - El↑

Where:

• E* = net energy/radiation

• E↓ = net downward radiation

• E↑ = net upward radiation

• Eg↓ = global solar radiation

• El↓ = downward longwave radiation

• Er↑ = reflected solar radiation

• El↑ = upward longwave radiation

Schematic of all components attributing to a net energy balance

Figure 3 Schematic of all components attributing to a net energy balance.
The global average of net radiation should be approximately zero throughout the year, or otherwise the earth’s average temperature will increase or decrease significantly. However, the local net radiation can vary considerably and plays a crucial role in understanding meteorological processes and monitoring the performance of solar energy systems. Using solar irradiance meters like pyranometers and pyrgeometers ensures you are measuring the components of the energy balance as accurately as possible. For a more practical approach on how to measure net radiation, you can read our article How to measure net radiation: a practical guide.