Atmospheric counter radiation

The atmospheric counter-radiation is the portion of the thermal radiation from the atmosphere that is radiated in the direction of the earth and whose energy thus remains in the earth's system. It is an important part of the energy balance on the surface and contributes to the greenhouse effect . It is called counter-radiation because it opposes the net radiation transport from the earth into space and thus reduces the radiation losses from the earth's surface. The size of the counter-radiation is to be interpreted differently depending on the branch of physics. In the quantum mechanical view, counter-radiation describes the heat radiation from the cold to the warm body - inextricably linked with the more intense radiation in the opposite direction. In the context of thermodynamic considerations, the counter-radiation denotes one of the terms in the radiation balance, so that all terms only depend on the temperature of one of the bodies under consideration. In the idealized greenhouse model , it is an essential part of the calculation.

description

The thermal radiation emanating from greenhouse gases and aerosols in a volume element depends on the local temperature , see Stefan-Boltzmann's law , and on the spectral transparency, see below. The radiation is emitted isotropically (uniformly in all directions). The counter-radiation reaching the ground originates for different wavelengths on average from different heights and thus temperature ranges. In the mid-infrared, a larger proportion of the radiation comes from cold space instead of the atmosphere when the sky is clear (see Atmospheric window ). The counter radiation therefore transports particularly little energy in this wavelength range. It is precisely in this area that the temperature of the earth's surface has the maximum radiation of a black body , which is a good model for the earth. It therefore receives less heat radiation from the atmosphere than it radiates and at night cools down slightly below the temperature of the air close to the ground. Then, depending on the weather conditions, dew , frost or ground frost can form.

Radiation sources

Atmospheric gases

The main constituents of the air ( N ₂ , O ₂ , Ar ) are IR-inactive , so they are neither stimulated nor emitted by thermal radiation . However, various polyatomic trace gases absorb and emit very intensively in characteristic absorption bands and thus represent greenhouse gases . Water vapor and ozone are angled molecules with a static dipole moment. Methane and carbon dioxide do not have a static dipole moment due to their symmetrical structure, but receive a transition dipole moment through vibration excitation and therefore emit.

Counter-radiation spectrum (blue) when the sky is clear

The consideration here in the long-wave infrared lying spectral lines do not arise during transitions between different energy levels of the electron shell , but during transitions between different rotational or vibrational states of the molecule (see molecular physics ). Such transitions typically produce a large number of closely spaced spectral lines in a limited wavelength range; such a collection of spectral lines is called a spectral band . Water vapor has an intense rotation-oscillation band in the range of 5 to 8 μm , while its rotation band covers the wavelengths above 17 μm. Carbon dioxide also has a very intense band between 13 and 17 μm. A relatively weak band of ozone is 9.6 μm.

The adjacent figure shows the described atmospheric band spectrum as the emission spectrum of air at an assumed temperature of 288 K (approx. 15 ° C, global average temperature). The bands shown here schematically as continuous areas (blue) actually consist of a large number of closely spaced and partially overlapping spectral lines. A comparison with the emission spectrum of a blackbody at the same temperature (light brown) shows that the air in the area of the bands emits almost as efficiently as the blackbody, but hardly at all in the gaps between the bands. In particular, there is a pronounced "window" in the range from around 8 to 13 μm, in which there is practically no emission (apart from the weak ozone band, there is only a very weak water vapor continuum in the window; the weak bands for methane and nitrous oxide fall in the range between 7 and 8 μm on the flank of the left water vapor band).

The total thermal radiation power emitted by the air is therefore less than the power emitted by a blackbody at the same temperature. Air is a radiant heater with relatively low efficiency.

Since a radiator absorbs well at those wavelengths at which it emits well, due to the kirchhoff's radiation law , the figure also shows the absorption spectrum of air versus thermal radiation.

That is why the emissions from the gases only travel a short free path before they are reabsorbed by the gases and emitted again. The radiation emitted from higher layers of air towards the ground is absorbed after a short distance by the lower layers of air and contributes to their warming, but does not reach the ground. It only gets there after several absorption and re-emission cycles. When the sky is clear, the counter-radiation that hits the ground comes from a maximum of a few hundred meters above sea level and thus from an air layer in which the temperature changes only slightly compared to the value close to the ground. For the radiation intensity arriving on the ground, the air temperature close to the ground is essential, such as the air temperature measured value determined by weather stations at a height of 2 m as standard.

Aerosols

Aerosols contained in the atmosphere (i.e. liquid droplets or small solids) do not emit line spectra, but rather continuous spectra (cf. the black body spectrum in the figure above) and therefore also emit in the gaps in the spectrum left by the emission lines of the gases. In sufficient concentration, they can significantly increase the total radiation and greatly reduce the radiation deficit compared to a black body (the sum of atmospheric and aerosol radiation cannot, however, for thermodynamic reasons be stronger than the radiation of a black body at any wavelength ).

Of particular importance are clouds , the water droplets or ice crystals of which are practically black bodies. In low-lying clouds, the temperature of the underside of the cloud ( condensation level ) corresponds to a good approximation of the dew point temperature measured by a weather station (usually at a height of 2 m) . If the cloud layer is sufficiently thick, the clouds radiate as black bodies at this temperature. For this reason, the earth's surface hardly cools down on cloudy nights - there is a radiation equilibrium.

Measurement

A pyrgeometer for measuring the counter radiation

So-called pyrgeometers are suitable for measuring the counter-radiation: A thermopile is housed in a protective housing, one end of which (the measuring surface) is blackened and directed towards the sky through a window, while the other end has thermal contact with the housing. The window equipped with an interference filter only allows radiation in the wavelength range from 5 to 25 μm to pass (especially no solar radiation). Due to its temperature, the measuring surface emits heat radiation towards the sky and receives the counter radiation from there. Depending on the balance between outgoing and incoming radiation, the measuring surface either heats up or cools down. The measurement voltage emitted by the thermopile is proportional to this change in temperature and allows the current radiation balance to be determined using a suitable calibration factor (e.g. −35.4 W / m²). With the case temperature measured separately at the same time, the device's own emissions can be determined using the Stefan-Boltzmann law . Since the measured radiation balance is the difference between counter-radiation and self-emission, the counter-radiation can be determined as the sum of the radiation balance and self-emission.

Course of the measured counter radiation on October 6, 2005

The red curve in the adjacent diagram shows the course of the counter-radiation measured in this way by a weather station near Munich on October 6, 2005. During the morning there was high fog . As efficient long-wave emitters, the fog droplets contributed to relatively high radiation values of approx. 370 W / m². Around noon the fog cleared, leaving a clear sky. The atmospheric gases alone are less efficient long-wave emitters, so the radiation values have dropped noticeably to around 300 W / m². The gray and blue curves were calculated for comparison for cloudy and clear skies using empirical radiation models (see below) from the simultaneously measured temperatures and humidity.

The variation in counter-radiation intensity that can be found in a typical location in Central Europe over the course of a year ranges from less than 200 W / m² on clear winter nights to well over 400 W / m² on overcast summer days. Averaged over the year and the entire globe, the intensity of the counter radiation is around 300 W / m². In comparison, the long-wave radiation of the earth's surface reaches about 373 W / m² on a global average (assuming a mean temperature of approx. 288 K), so that the earth is subject to an average loss of about 70 W / m² due to long-wave radiation.

A measurement of u. a. the atmospheric counter-radiation takes place z. B. at the 50 stations of the World Radiation Monitoring Center .

Computational modeling

Since the radiation mechanisms are subject to known physical laws and the radiation properties of greenhouse gases have been well researched, the counter-radiation intensity can in principle be determined by model calculations instead of direct measurements, provided that the state of the atmosphere is known with sufficient accuracy. If, for example, one knows the state of the atmosphere at different heights, the counter-radiation near the ground can be determined quite precisely using calculation methods that describe the radiation transport in the atmosphere, which is emitting and absorbing at the same time. However, the effort required to obtain the atmospheric data (e.g. radiosonde ascents ) limits the advantage of the method.

Because of the short range of long-wave radiation in the atmosphere, the counter-radiation arriving on the ground comes from a maximum height of a few hundred meters (see above ), so that a good estimate of the radiation intensity is possible with knowledge of the state of the atmosphere close to the ground. Various empirical formulas have been developed for this purpose. The main influencing factor is temperature. The air temperature measured by weather stations at a height of 2 m is usually available here. The change in temperature over the relevant altitude range is small and can be taken into account using suitable empirical formula parameters. The concentrations of most greenhouse gases are more or less constant and can also be recorded using fixed parameters. Only the water vapor content is highly variable, which is why some formulas take air humidity into account as an input variable. In addition to the radiation component of the clear sky that can be estimated in this way, there may be an additional contribution from cloud cover.

The counter radiation in a cloudless sky can be estimated , for example, using the Ångström formula :

{\ displaystyle A _ {\ mathrm {g, k}} \, = \, \ sigma \, T _ {\ mathrm {St}} ^ {4} \, (0 {,} 790-0 {,} 174 \ cdot 10 ^ {- 0 {,} 041 \ mathrm {hPa} ^ {- 1} \ cdot e})}

When the sky is completely cloudy and the clouds are low, the temperature of the underside of the cloud ( condensation level ) corresponds to a good approximation of the dew point temperature measured by a weather station (usually at a height of 2 m). The clouds emit as black bodies with this temperature:

{\ displaystyle A _ {\ mathrm {g, w}} \, = \, \ sigma \, T _ {\ mathrm {d, St}} ^ {4}}

The counter-radiation of a partly cloudy sky is composed proportionally of the contributions of the cloud undersides and the clear sky surfaces:

{\ displaystyle A _ {\ mathrm {g}} \, = \, N \ cdot A _ {\ mathrm {g, w}} + (1-N) \ cdot A _ {\ mathrm {g, k}}}

With:

${\ displaystyle A _ {\ mathrm {g}}}$ : atmospheric counter radiation
${\ displaystyle A _ {\ mathrm {g, k}}}$ : atmospheric counter-radiation with a cloudless sky
${\ displaystyle A _ {\ mathrm {g, w}}}$ : atmospheric counter radiation when the sky is overcast
${\ displaystyle \ sigma}$ : Stefan-Boltzmann constant
${\ displaystyle T _ {\ mathrm {St}}}$ : Station temperature (at a height of 2 m)
${\ displaystyle T _ {\ mathrm {d, St}}}$ : Dew point temperature at station height
${\ displaystyle e}$ : Water vapor partial pressure at the station
${\ displaystyle N}$ : Degree of coverage

The counter-radiation values calculated using these formulas from air temperature and air humidity for a completely clear and a completely covered sky are shown in the diagram of the previous section for comparison with the measured values (blue and gray curve). As can be seen, the measurement curve agrees well with the values calculated for cloudy skies during the cloudy morning and well with the values calculated for clear skies after clearing up. In the evening the clouds apparently increased again.

Radiation balance

At night with a clear sky

When the sky is clear, the counter-radiation mainly consists of the thermal radiation of the atmospheric gases. The temperature relevant for the emission is practically identical to the air temperature close to the ground and thus similar to the temperature of the ground, which is also radiating. The ground, however, emits practically as a black body, while the intensity of the atmospheric radiation is significantly lower due to the gaps in the emission spectrum, despite the similar temperature.

The terrestrial radiation can therefore only partially be compensated by the atmospheric counter-radiation and the earth's surface cools: clear nights are particularly cool. The earth's surface and other terrestrial surfaces (house roofs, house facades, car windows, etc.) can cool down not only below the air temperature, but even below the dew point temperature. The consequences of this nocturnal hypothermia are condensation and frost formation in winter .

In the desert climate , the air contains only small traces of the greenhouse gas water vapor; the counter-radiation has a particularly low intensity and desert nights are very cold.

The dew caps attached to telescopes have the purpose of reducing the radiation loss and thus the hypothermia of the objective lens by covering part of the sky in the field of view of the lens. From this area of the sky, the lens receives radiation from the well-radiating dew cap instead of the lower radiation from the atmosphere, which is almost equally warm but less radiant.

At night when the sky is overcast

When the sky is overcast, the counter radiation is noticeably more intense because of the contribution of the clouds. Since the average relative humidity at night in temperate latitudes is around 80% and more, the dew point temperature that is decisive for the counter-radiation of the clouds is only slightly below the air temperature.

The ground, which is also about air temperature, is now opposed to well-radiating clouds of similar temperature. The radiation balance is almost balanced and the earth's surface cools down only a little: Overcast nights are warmer, there is little or no dew.

During the day

During the day, depending on the degree of cloudiness, there is a more or less unbalanced balance of terrestrial radiation and atmospheric counter-radiation. However, the short-wave solar radiation that also falls during the day is mainly absorbed by the ground and far less by the atmosphere, so that the surface temperature rises above the air temperature. The entire long- and short-wave radiation balance is now positive for the earth.

example

Frosted blades of grass

With counter radiation, the phenomenon described below is a rare occurrence. Without the existence of the counter-radiation (or the equivalent view that the heat flow from a warm to a cooler body also depends on the temperature of the cooler body) the phenomenon described below would occur almost every night.

Look at a blade of grass on a clear, windless autumn night. The air temperature is +5 ° C, the air humidity 90%, the convective heat transfer coefficient 5 W / m²K, the emissivity of the grass 0.95. The underside of the stalk is in radiation equilibrium with the stalks underneath at the same temperature, the upper side radiates against the clear sky. It gains the atmospheric counter-radiation as well as the convective heat flow from the ambient air and loses its own thermal emission according to the Stefan-Boltzmann law . So your energy balance is:

{\ displaystyle E \, = \, \ varepsilon \, A _ {\ mathrm {g, k}} + \ alpha _ {k} (\ vartheta _ {\ mathrm {L}} - \ vartheta _ {\ mathrm {O }}) - \ varepsilon \, \ sigma \, \ vartheta _ {\ mathrm {O}} ^ {4}}

With

${\ displaystyle \, E}$	Energy balance, W / m²
${\ displaystyle \, A _ {\ mathrm {g, k}}}$	atmospheric counter-radiation with a cloudless sky, W / m²
${\ displaystyle \, \ alpha _ {k}}$	convective heat transfer coefficient, W / m²K
${\ displaystyle \, \ varepsilon}$	Emissivity of the surface, 0… 1
${\ displaystyle \, \ vartheta _ {\ mathrm {L}}}$	Air temperature, K
${\ displaystyle \, \ vartheta _ {\ mathrm {O}}}$	Surface temperature, K

Under the given conditions the water vapor partial pressure is 7.85 hPa, the atmospheric counter-radiation is 240 W / m². The thermal emission of the surface, which is initially at 5 ° C, initially amounts to 322 W / m². Since the surface loses more heat than it gains, it cools down. The emission losses decrease due to the falling temperature, while the convective heat influx increases due to the increasing temperature difference between surface and air. As soon as thermal equilibrium has been established, the energy balance is zero (losses and gains cancel each other out) and solving the balance equation provides the surface temperature . ${\ displaystyle \ vartheta _ {\ mathrm {O}} = - 5 {,} 1 \, ^ {\ circ} \ mathrm {C}}$

The blade of grass is therefore noticeably undercooled below the air temperature. It not only falls below the dew point temperature of the air (+3.5 ° C), so that dew precipitates, it also falls below the freezing point , so that the dew is deposited as frost (if the frost continues, the latent heat released would have to be taken into account in the energy balance) . It occurs ground frost (concretely radiation Frost ), although the air temperature is well above the freezing point.

In practice, the hypothermia is usually less than in this simplified example. The heat capacity of a thermally inert surface, heat reserves absorbed during the day and latent heat released as a result of the formation of dew or frost can delay cooling. Wind increases the convective heat supply and reduces hypothermia. In particular, the radiation losses of the radiating surface can be reduced if there are terrestrial objects in its field of view. Due to their better radiation properties, such objects emit more radiation (terrestrial counter-radiation) than the air, even if they are not warmer than the air. Plants can be protected from radiation frost by covering them with a tarpaulin, because the tarpaulin (although it itself only has air temperature) radiates more strongly than the air. Plants that are placed in a “protected” place in a wall corner see less sky and lose less heat radiation.

The example illustrates the microclimatic consequences of the fact that the air is a relatively poor heat emitter. On the other hand, the fact that the air emits heat radiation at all has considerable macroclimatic consequences. If you repeat the above calculation for the hypothetical case , you get a cooling of the now uncompensated radiating surface to −32 ° C. Such pronounced nocturnal hypothermia below the air temperature would contradict any everyday experience. The warming effect of the atmospheric counter-radiation is therefore of considerable importance. This effect is known as the natural atmospheric greenhouse effect . ${\ displaystyle A _ {\ mathrm {g, k}} = 0}$

Greenhouse effect

Main article: greenhouse effect

The earth's surface absorbs about 175 W / m² of solar radiation on a global and long-term average. Since the earth - apart from climatological fluctuations - neither warms up nor cools down significantly in the long term, it is evidently in radiation equilibrium with the sun and has to give off an average heat flow of the same amount. The mean temperature of the earth's surface is around 288 K. If one considers the earth, admittedly considerably simplified, as a sphere with a uniform surface temperature, according to the Stefan-Boltzmann law (at 288 K and an assumed emissivity of 0.95) it radiates a heat output of 373 W. / m², which is well above the irradiation and seems to violate the radiation equilibrium.

The discrepancy resolves when the radiation contribution from the atmosphere is taken into account. The ground receives on average not only 175 W / m² of solar radiation, but also 300 W / m² of counter radiation. With a total of 475 W / m² radiation gain and 373 W / m² radiation loss, the ground has a heat gain of around 100 W / m², which it emits to the atmosphere via convection and evaporation . The energy balance of the earth's surface is preserved thanks to the atmospheric counter-radiation despite the relatively high surface temperature.

On a global average, the earth receives almost twice as much heat radiation (300 W / m²) from the atmosphere than from the sun (175 W / m²). If this radiation from the atmosphere did not exist, the energy balance would only allow a considerably lower heat radiation and thus a lower surface temperature. The usual rough calculation uses the solar heat gains absorbed by the earth and the atmosphere (with a planetary albedo of 30% a total of about 240 W / m²) and finds that without the greenhouse effect, they are combined with heat radiation at −15 ° C (assumed emissivity 0.95) or −18 ° C (emissivity 1.0) are in equilibrium. The 30 K temperature difference to the actual conditions is attributed to the greenhouse effect.

The situation of a planet with an atmosphere but without a greenhouse effect must be differentiated from the situation without an atmosphere, as can be found on the moon, for example. An atmosphere scatters some of the light back into space, which increases the albedo compared to a body without an atmosphere. The absorption-related solar heat gain of the soil, which is almost exclusively affected by direct radiation, is higher without an atmosphere. For a surface albedo of 10%, mean surface temperatures of 0 ° C (emissivity 0.95) or −3 ° C (emissivity 1) result. An atmosphere, and to an even greater extent cloud cover, reduces the proportion of direct radiation due to an increased albedo, but increases the incident radiation power near the ground and thus the ground temperature through the associated counter-radiation, because the ground then only becomes more balanced through a higher temperature Radiation balance can achieve. In addition to the effects of albedo and counter-radiation, an atmosphere also has a balancing effect on the temperature profile and regional temperature distribution: winds transport energy (mostly towards the poles) and the heat capacity of the atmosphere reduces the temperature difference between day and night temperatures.

The greenhouse effect just described is a natural consequence of the atmospheric properties and, with its effects on the temperature conditions of the earth, an essential prerequisite for the development of the biosphere. Changes in the greenhouse effect are part of the changes in the radiation budget compared to the reference year 1750, which are summarized as radiative forcing.

literature

S. Arrhenius (1896): On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground . In: Philosophical Magazine and Journal of Science 41, No. 251, 1896, pp. 237–276 ( PDF ( Memento of October 6, 2014 in the Internet Archive ) 4.1 MB; the first quantitative study of the contribution of carbon dioxide to the greenhouse effect) .
K. Blümel et al .: Development of test reference years (TRY) for climatic regions of the Federal Republic of Germany . BMFT, Research Report T 86-051, 1986.
R. Geiger, RH Aron, P. Todhunter: The Climate Near the Ground . 5th edition, Vieweg, Braunschweig 1995, ISBN 3-528-08948-2 .
H. Häckel: Meteorology . Ulmer, Stuttgart 1999, ISBN 3-8001-2728-8 .
MG Iziomon, H. Mayer, A. Matzarakis: Downward atmospheric longwave irradiance under clear and cloudy skies: Measurement and parameterization . Journal of Atmospheric and Solar-Terrestrial Physics 65 (2003), pp. 1107–1116 ( PDF ( Memento from January 12, 2006 in the Internet Archive ), 325 kB).
GH Liljequist, K. Cehak: General Meteorology . 3rd edition, Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig / Wiesbaden 1984, ISBN 3-540-41565-3 .
H. Malberg: Meteorology and Climatology. An introduction . 4th edition, Springer-Verlag, Berlin / Heidelberg / New York 2002, ISBN 3-540-42919-0 .
F. Möller: Introduction to Meteorology . Volume 2: Physics of the atmosphere . Bibliographisches Institut, Mannheim 1973, ISBN 3-411-00288-3 .
W. Roedel: Physics of our environment: The atmosphere . 3. Edition. Springer, Berlin / Heidelberg 2000, ISBN 3-540-67180-3 , 1.3 Terrestrial radiation, p. 38-41 .
U. Wolfseher: The heat transport on component surfaces with special consideration of the long-wave radiation exchange . Health engineer - building technology - building physics - environmental technology 102 (1981) issue 4, pp. 184-200.

Web links

Earth's radiation budget and Greenhouse Effect, archive.org Memento, Dec. 28, 2010

Individual evidence

^ R. Geiger, RH Aron, P. Todhunter: The Climate Near the Ground. 5th ed., Vieweg, Braunschweig 1995, ISBN 3-528-08948-2 , p. 11: "Longwave radiation emitted by the atmosphere G is termed counterradiation (sometimes called longwave irradiance or atmospheric radiation) since it counteracts the terrestrial radiation loss from the surface. "
↑ Lecture material by Prof. W. de Boer from the University of Karlsruhe on the subject of rotation and vibration of molecules (SS 2005) ( Memento from June 21, 2007 in the Internet Archive )
^ F. Möller: Introduction to Meteorology . Volume 2: Physics of the atmosphere . Bibliographisches Institut, Mannheim 1973, ISBN 3-411-00288-3 , p. 51.
^ W. Roedel: Physics of our environment: The atmosphere . 2nd edition, Springer, Berlin 1994, ISBN 3-540-57885-4 , p. 40.
^ R. Geiger, RH Aron, P. Todhunter: The Climate Near the Ground . 5th edition, Vieweg, Braunschweig 1995, ISBN 3-528-08948-2 , p. 21.
↑ Kipp & Zonen (Ed.): Instruction Manual CG1 / CG2 Pyrgeometer / Net Pyrgeometer . Delft 1992.
^ H. Häckel: Meteorologie . Ulmer, Stuttgart 1999, ISBN 3-8001-2728-8 , p. 184, tab. 14.
↑ ^a ^b ^c ^d ^e ^f ^g ^h W. Roedel: Physics of our environment: The atmosphere . 2nd edition, Springer, Berlin 1994, ISBN 3-540-57885-4 , p. 37f.
^ F. Möller: Introduction to Meteorology . Volume 2: Physics of the atmosphere . Bibliographisches Institut, Mannheim 1973, ISBN 3-411-00288-3 , p. 53.
↑ ^a ^b K. Blümel et al .: Development of test reference years (TRY) for climatic regions of the Federal Republic of Germany . BMFT, Research Report T 86-051, 1986, p. 73 (with correction of a sign error).

This version was added to the list of articles worth reading on May 24, 2009 .

[1] R. Geiger, RH Aron, P. Todhunter: The Climate Near the Ground. 5th ed., Vieweg, Braunschweig 1995, ISBN 3-528-08948-2 , p. 11: "Longwave radiation emitted by the atmosphere G is termed counterradiation (sometimes called longwave irradiance or atmospheric radiation) since it counteracts the terrestrial radiation loss from the surface. "

[2] Lecture material by Prof. W. de Boer from the University of Karlsruhe on the subject of rotation and vibration of molecules (SS 2005) ( Memento from June 21, 2007 in the Internet Archive )

[MoellerS51-3] F. Möller: Introduction to Meteorology . Volume 2: Physics of the atmosphere . Bibliographisches Institut, Mannheim 1973, ISBN 3-411-00288-3 , p. 51.

[4] W. Roedel: Physics of our environment: The atmosphere . 2nd edition, Springer, Berlin 1994, ISBN 3-540-57885-4 , p. 40.

[5] R. Geiger, RH Aron, P. Todhunter: The Climate Near the Ground . 5th edition, Vieweg, Braunschweig 1995, ISBN 3-528-08948-2 , p. 21.

[6] Kipp & Zonen (Ed.): Instruction Manual CG1 / CG2 Pyrgeometer / Net Pyrgeometer . Delft 1992.

[7] H. Häckel: Meteorologie . Ulmer, Stuttgart 1999, ISBN 3-8001-2728-8 , p. 184, tab. 14.

[RoedelS37-8] ↑ ^a ^b ^c ^d ^e ^f ^g ^h W. Roedel: Physics of our environment: The atmosphere . 2nd edition, Springer, Berlin 1994, ISBN 3-540-57885-4 , p. 37f.

[MoellerS53-9] F. Möller: Introduction to Meteorology . Volume 2: Physics of the atmosphere . Bibliographisches Institut, Mannheim 1973, ISBN 3-411-00288-3 , p. 53.

[Blümel_1986_73-10] K. Blümel et al .: Development of test reference years (TRY) for climatic regions of the Federal Republic of Germany . BMFT, Research Report T 86-051, 1986, p. 73 (with correction of a sign error).