Symbolic Cholesky decomposition

File:Pyrgeometer CGR4 instrument.gif

Example of a pyrgeometer

A pyrgeometer is a device that measures the atmospheric infra-red radiation spectrum that extends approximately from 4.5 µm to 100 µm.

Pyrgeometer components

File:Pyrgeometer CGR4 kippzonen.gif

Example of a pyrgeometer showing the principal components

A pyrgeometer consists of the following major components:

• A thermopile sensor which is sensitive to radiation in a broad range from 200 nm to 100 µm

• A silicon dome or window with a solar blind filter coating. It has a transmittance between 4.5 µm and 50 µm that eliminates solar shortwave radiation.

• A temperature sensor to measure the body temperature of the instrument.

• A sun shield to minimize heating of the instrument due to solar radiation.

File:Pyrgeometer CGR4 transmittance.gif

Typical combined window and solar blind filter transmittance for CGR 4 model pyrgeometer

Measurement of long wave downward radiation

The atmosphere and the pyrgeometer (in effect its sensor surface) exchange long wave IR radiation. This results in a net radiation balance according to:

$\ E_{net}={\ E_{in}-\ E_{out}}$

Where:
$E_{net}$ - net radiation at sensor surface [W/m²]
$E_{in}$ - Long-wave radiation received from the atmosphere [W/m²]
$E_{out}$ - Long-wave radiation emitted by the sensor surface [W/m²]

The pyrgeometer's thermopile detects the net radiation balance between the incoming and outgoing long wave radiation flux and converts it to a voltage according to the equation below.

$\ E_{net}={\ U_{emf} \over \ S}$

Where:
$E_{net}$ - net radiation at sensor surface [W/m²]
$U_{emf}$ - thermopile output voltage [V]
$S$ - sensitivity/calibration factor of instrument [V/W/m²]

The value for $S$ is determined during calibration of the instrument. The calibration is performed at the production factory with a reference instrument traceable to a regional calibration center.

To derive the absolute downward long wave flux, the temperature of the pyrgeometer has to be taken into account. It is measured using a temperature sensor inside the instrument, near the cold junctions of the thermopile. The pyrgeometer is considered to approximate a black body. Due to this it emits long wave radiation according to:

$\ E_{out}={\sigma *\ T^{4}}$

Where:
$E_{out}$ - Long-wave radiation emitted by the earth surface [W/m²]
$\sigma$ - Stefan-Boltzmann constant [W/(m²·K⁴)]
$T$ - Absolute temperature of pyrgeometer detector [kelvins]

From the calculations above the incoming long wave radiation can be derived. This is usually done by rearranging the equations above to yield the so-called pyrgeometer equation by Albrecht and Cox.

$\ E_{in}={\ U_{emf} \over \ S}+{\sigma *\ T^{4}}$

Where all the variables have the same meaning as before.

As a result, the detected voltage and instrument temperature yield the total global long wave downward radiation.

Usage

Pyrgeometers are frequently used in meteorology, climatology studies. The atmospheric long-wave downward radiation is of interest for research into long term climate changes.

The signals are generally detected using a data logging system, capable of taking high resolution samples in the millivolt range.

References

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See also

• pyranometer
• radiometer