A calibration of Langley lunar data
by Hans Erren, Posted 11 August 2003, Revised 10 September 2003
Allegheny Moon it’s up to you
Please see what you can do 
Goal of this paper
The key paper on global warming written by Svante Arrhenius  in 1896 relies on the infrared observations of the moon as published by Langley in 1890. The paper of Langley contains errors that were corrected in 1900 by Langley and Abbot but this was after Arrhenius published his theory.
I recalibrate Langley's original data with modern observations and standard atmospheric models using modtran3 online radiation code.
The first fact that has to be put right is that Langley omitted Frank W. Very as co-author in his publication of 1890 , Very is the leading observer and processor of all Lunar data in this work, and Langley acknowledges his error on page 212:
fig 1: Langley acknowledges Very
Dispersion of a rock salt prism
Langley and Very use rocksalt (NaCl) prisms to create an infrared spectrum as glass is opaque at infrared wavelengths. Here is the setup of the instruments.
fig 2: Instrumental setup from plate 4. M=Mirror, S=Slit, L=Lense(2x), P=Prism, B=Bolometer
The angle of deviation d can be obtained by applying Snell's law on the prism geometry. d = q +arcsin(n sin(A-arcsin((sinq )/n)))-A               (1)
where n = refractive index, A = prism top angle and q = minimum deviation angle.
A and q are observational values but the refractive index n beyond wavelengths of about 5 micron was not exactly known in 1890. Langley and Very relied on an extrapolation of near infrared values and made a large error in the mid infrared. It was only the work of Paschen that showed that the refractive index curved back in the mid infrared. this was acknowledged by Langley and Abbot in 1900 but this was after Arrhenius had published his work in 1896. A comparison of refractive indices is shown in an adaptation from plate 20 in Langley and Abbott.
fig 3: Langleys refractive index measurements and his extrapolation in 1886 (both highlighted in orange) compared with later work (adapted from plate 20 in Langley and Abbot 1900)
The fitting curve in figure 3 is from Ketteler, using Langley and Abbot parameters (page 261),
fig 4: Langley and Abbot parameters for Ketteler.
which is also fitting modern data
fig 5: Modern values of refractive index compared with Ketteler.
Applying Ketteler on equation (1), yields the deviation angle as function of wavelength (neglecting the refractive index of air). As comparison the old theory of Cauchy is given which yields good fit in the visible part but is useles in the infrared, as Langley found out in 1886. Also Langley's 1886 extrapolation is given.
fig 6: NaCl prism deviation according to Cauchy, Langley and Ketteler (= Langley 1900).
The extrapolation of Langley was much used, although Langley himself had warned about it in earlier work. Here is his footnote 2 on page 255 of Langley and Abbot 1900:
fig 7: Langley regretting people running away with his extrapolation.
Langley's 1886 extrapolation error has a long life: Due to Arrhenius, Ramanathan and Vogelmann in 1997 assumed that Langley observed well up to 30 micron (which btw is physically impossible as NaCl becomes opaque at 20 micron ).
The Allegheny observations of 9 February 1887
The first mistake that needs to be put aside is the fact that the data in Arrhenius 1896 are lunar spectra. The data used are moon minus sky observations. For lunar work the bolometer was working at the very detection limit of the instrument. Here are the raw bolometer readings of 9 February 1887.
fig 8: Raw bolometer readings of 9 february 1887.
What is evident from this dataset is that the absolute value of the bolometer readings are very erratic. A measuring sequence has the following steps:
A series is a set from high deviation angle to low deviation angle and back. On 9 February 1887 four series were observed:
- set the deviation angle at the desired position
- take a 12 second reading from a reference screen of temperature 18ºC (screenA)
- take a 12 second reading from the sky to the right of the moon(skyB)
- take a 12 second reading from the moon(moonC)
- take a 12 second reading from the sky to the left of the moon(skyC)
- take a 12 second reading from a reference screen of temperature 18ºC (screenE)
- I 41.1417 40 38.3333 38 37.5833 37 36.6667 36 36 36.6667 37 37.5833 38 38.3333 40
- II 41.1417 40.3333 40 39.6667 39.3333 39 38.6667 38.5 38.3333 38.1667 38 37.8333 37.6667 37.5 37.3333 37.1667 37 36 35 35 36 37 37.1667 37.3333 37.5 37.6667 37.8333 38 38.1667 38.3333 38.5 38.6667 39 39.3333 39.6667 40 40.3333 41.1417
- III 40 38.3333 38 37.5833 37 36.6667 36 36 36.6667 37 37.5833 38 38.3333 40
- IV 40 38.3333 38 37.5833 37 36.6667 36 36 36.6667 37 37.5833 38 38.3333 40
Only when a reduction is made the data are starting to make sense. The following graph shows a reduction moonC-(skyB+skyD)/2 of all four series:
fig 9: Reduced bolometer readings (moon-sky) of 9 february 1887.
Reconstructing the Allegheny observations using modtran3
For starters here is a recent "lunar infrared spectrum"
fig 10: High resolution calibrated atmospheric spectrum using the moon as light source.
With permisson of J. Notholt, Institute of Environmental Physics, University of Bremen, Germany.
The radiation code of Modtran3 to calculate infrared atmosphere spectra was put online by David Archer and Ray Pierrehumbert. To create a moon sky residual the following steps were taken.
- calculate an upward looking radiation spectrum for mid-latitude summer and winter using modtran 3 (sensor altitude 0)
- create a lunar emission curve of 108º C using planck's radiation law P
- the last column in the modtran output is the transmission spectrum T
- multiply the transmission spectrum with the plack curve T*P
- take the sky spectrum (ninth column in modtran output) S
- the moon signal is Ö(S2+(T*P)2)
- the residual signal is Ö(S2+(T*P)2) - S
fig 11: summer and winter spectra from modtran3
The next step is to compare modtran with Allegheny, for this the modtran data was mapped to deviation angle using figure 6. The amplitude of the Allegheny data was scaled with an arbitrary factor of 1/800000
fig 12: modtran3 spectra compared with Allegheny observations
The data lower than 6 micron is due to solar emission scattering from the moon. The statement of Baliunas and Soon  that Langleys data go up to only 3 micron could be based on Solar spectra by Langley (see langley and Abbot for a nice example)
- The Allegeny data show infrared observations between 0.9 and 13 micron
- The data between 0.9 and 6 micron is due to sunlight scattering on the surface of the moon
- Ramanathan and Vogelmann are wrong in stating that Langley's data spanned 0.9-30 micron
- Baliunas and Soon are wrong in stating that Langley's data spanned 0.3 - 3
- The Allegheny data show a remarkable weak ozone effect
- The Allegheny data are showing a strong influence of water vapour
- The Allegheny data are of little use to calculate the influence of CO2 on climate
- so shine... shine... shine...
 Svante Arrhenius, 1896, On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground, The London, Edinburgh, and Dublin Philosophical Magazine and Jounal of Science [fifth series] April 1896. vol 41, p237-275, Online scanned document (Warning, 27.1 Mb pdf)
 Samuel P. Langley (and Frank W. Very),1890 , The Temperature of the Moon, Memoir of the National Academy of
Sciences, vol. iv. 9th mem. 193pp .
 Langley & Abbot, 1900, Annals of the Astrophysical Observatory of the
Smithsonian Institution, Volume I, Online scanned document
 David Archer and Ray Pierrehumbert, [undated] , MODTRAN3 Atmospheric Radiation Code, University of Chicago Department of the Geophysical Sciences, http://geosci.uchicago.edu/~archer/cgimodels/radiation.html
Data source for NaCl optical properties:
 Ramanathan, V. and A.M. Vogelmann.(1997) Greenhouse effect, atmospheric
solar absorption and the Earth's radiation budget: From the
Arrhenius/Langley era to the 1990s. AMBIO, 26(1):38-46
 Dick Manning and Al Hoffman (Words and Music), (ca 1956), Allegheny Moon, Artist: Patti Page (peak Billboard position # 2 in 1956), http://www.elyrics4u.com/a/allegheny_moon_patti_page.htm
Sallie Baliunas and Willie Soon , (1999) Cutting Edge: Pioneers in the Greenhouse Effect, World Climate report, vol 4 no 19
Arrhenius original tables:
Arrhenius was wrong: