Symbolic Cholesky decomposition

2013-12-09T08:53:33Z

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[[Image:pyrgeometer CGR4 instrument.gif|thumb|right|450px|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 ==

[[Image:pyrgeometer CGR4 kippzonen.gif|thumb|right|450px|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.

[[Image:pyrgeometer CGR4 transmittance.gif|thumb|right|450px|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:

 
:<math>
\ E_{net} = { \ E_{in} - \ E_{out} }
</math>

Where:
 
<math>E_{net}</math> - net radiation at sensor surface [W/m²] 
<math>E_{in}</math> - Long-wave radiation received from the atmosphere [W/m²] 
<math>E_{out}</math> - 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.
 
:<math>
\ E_{net} = { \ U_{emf} \over \ S}
</math>

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

The value for <math>S</math> 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.<ref>{{cite web
|url=http://www.pmodwrc.ch/pmod.php?topic=irc |title=IRC-Infra red radiation calibration center Davos}}</ref>

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:
 
:<math>
\ E_{out} = { \sigma * \ T^4}
</math>
 
Where:
 
<math>E_{out}</math> - Long-wave radiation emitted by the earth surface [W/m²] 
<math>\sigma</math> - [[Stefan-Boltzmann constant]] [W/(m²·K4)] 
<math>T</math> - 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.

:<math>
\ E_{in} = { \ U_{emf} \over \ S }+ {\sigma * \ T^4}
</math>

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==
{{Reflist}}

==See also==
* [[pyranometer]]
* [[radiometer]]

{{Meteorological equipment}}

[[Category:Electromagnetic radiation meters]]
[[Category:Radiometry]]

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Symbolic Cholesky decomposition