The Ångströms: Inventors of Pyrgeometer and DLR

The Swedish meteorologist Anders Ångström (1888-1981), son of the physicist Knut Ångström, son of the famous physicist Anders Jonas Ångström founder of spectroscopy, reported in A Study of the Radiation of the Atmosphere (1915) measurements using a pyrgeometer, designed by his father (1905),  of "effective radiation" E_eff between the atmosphere and the Earth surface with

• E_eff = E_in - E_out 
• E_out = blackbody radiance from surface to space = sigma T^4 with T surface temperature
• E_in = DLR = downwelling long wave radiance from atmosphere to surface,    

where sigma is the constant of the Stefan-Boltzmann Law of blackbody radiation. 

The pyrgeometer equipped with a thermocouple reads a voltage U_emf  from which R_eff is computed as U_emf/S, where S is a sensitivity factor determined by calibration to a reference. The voltage is proportional to the difference between the temperature of the surface and that of the atmosphere as measured by the pyrgeometer detector. 

Anders Ångström thus reported in 1915 measurements of a quantity named DLR or "back radiation" according to the formula

• DLR =  U_emf/S + sigma T^4         (*)

defining DLR by an instrument reading of U_emf/S and Stefan-Boltzmann's Law for blackbody radiation into a surrounding at 0 K. The formula (*) defining back radiation = DLR through an instrument, is presented as a basic pillar of the greenhouse effect GHE with the trace CO2 given the capability to change DLR with a warming effect on the Earth surface. 

Anders Ångström constructed his pyrogeometer from an idea of two-way heat flux E_in and E_out, while understanding that only the net flux E_eff could effectively be measured.  But to determine DLR = E_in from (*)  E_out had to be known and Ångström then simply assumed that E_out = sigma T^4 as if the Earth surface was radiating like a blackbody into a surrounding of 0 K.  Since this is obviously not the case Ångström made an ad hoc assumption about E_out without physical basis, and then reported DLR with a terminology suggesting a physical meaning. But the DLR determined by (*) lacks physical meaning because E_out lacks physical meaning. 

Anders Ångström thus opened to an unphysical misconception of two-way radiative heat transfer, while according to Stefan-Boltzmann there is only one-way heat transfer from warm to cold. Anders was not a physicist like his father Knut, and evidently lacked some understanding of the physics of the pyrgeometer.

The unphysical science by Anders Ångström opened to give the atmospheric trace gas CO2 an unphysical warming effect which was later efficiently exploited by climate alarmists.  

To understand that a pyrgeometer reporting DLR in W/m2, while effectively recording a temperature difference,  is reporting fiction without physical basis, requires going to the bottom of the Stefan-Boltzmann Law and its proof. Since very few people are willing to do so, a constructive debate is lacking. 

Both climate alarmists and most of their critics have been misled by Anders Ångström and take for granted that there is something named DLR of some physical meaning which can be connected to CO2 which is evidenced by pyrgeometers. And without critics, climate alarmism continues to oppress humanity, without reason in physics.

Arrhenius vs Ångström vs Stefan-Boltzmann

In our search for the origin of the misinterpretation of Stefan-Boltzmann's Law behind DLR and GHE as two-way heat transfer, we were led to the Swedish meteorologist Anders Ångström. In 1900 his father Knut Ångström expressed strong criticism of the possible warming effect of CO2 suggested by Svante Arrhenius (1896).  In his article Arrhenius referred to Stefan-Boltzmann's  Law with one-way radiative heat transfer from a body temperature T1 to a body of lower temperature T2 being proportional to (T1^4 -T2^4), as illustrated in the following clip with the important qualification of emission into empty space corresponding to T2=0:

Arrhenius thus used a correct version of Stefan-Boltzmann's Law with one-way heat transfer from warm to cold without DLR, while Anders Ångtröm suggested an empirical formula for DLR reminiscent of an incorrect two-way form of Stefan-Boltzmann's Law. Climate alarmism eventually picked up CO2 from Arrhenius and DLR from Anders Ångström.

(this post has been updated)

The Inventors of DLR and thus GHE

Tracing the history of the corner stone of the greenhouse effect GHE in the form of downwelling long wave radiation DLR from the atmosphere to the Earth surface with a supposed warming effect from in particular CO2, leads to

• Notes on Radiation in the Atmosphere by D. Brunt (1932)  
• On the Variation of the Atmosphere Radiation by Anders Ångström (1925)

where we find the following empirical formulas:

• DLR = (a - b 10^(-ce)) sigma T^4 (Anders Ångström)
• DLR = (a + be^0.5) sigma T^4 (Brunt)

where T is temperature and e is the vapor pressure at a 2m level above the Earth surface, and a, b and c are coefficients determined by calibration with some reference. These formulas appear to be conceived as variations of Stefan-Boltzmann's Law R = sigma T^4, expressing the radiation from a blackbody of temperature into a background at 0 K.

Ångström and Brunt thus introduced a quantity later named DLR, which could be computed according to a formula expressing a heat flux from the atmosphere to the Earth surface, which was later picked up by Brutsaert (1975) and others and formed into GHE with the effect coming from DLR and CO2. 

At the origin of climate alarmism we find three Swedes: Arrhenius(1896), Anders Ångström(1925) followed by Bert Bolin as founder of IPCC.  All three have passed away and can no longer be held responsible, but their living active followers are.

PS Knut Ångström (1900) questioned (father of Anders) the warming effect of CO2 claimed by Arrhenius (1896), but his son Anders contributed to GHE by his empirical formula for DLR.