^{1,2}. MILIA is a free use site and is the only free online source of OLR data that is available, as far as we know, so that it has been used as a test of a simple model for the CO

_{2}no feedback climate sensitivity

^{3}. The MILIA website has been in existence since 1995.

However, up until May of 2017, the MILIA web site had an underlying Planck Function which spanned a limited range of wavenumbers of 100 wn to 1500 wn. Such a limited wavenumber range results in significant errors for certain quantities that are important in environmental of climate science courses. The new version described here extends the range of the underlying Planck distribution to 100 wn – 2200 wn.

The Fig. 1, at the end of this write up, shows a comparison between the old version of MILIA and the new version for GHG at default concentration. It corresponds to an observer looking downward from 20 km, with GHG concentrations of 400 PPM CO_{2} , 1.7 PPM CH_{4}, 28 ppb tropical ozone, Strat Ozone scale 1, and water vapor scale 1. The left panel represents results before May 2017, The right panel results after May 2017.

In the following we describe some “key results” obtained before and after the new version of MILIA.

1. An important result in basic environmental physics courses is the following: If there were no Greenhouse Effect, and assuming an albedo of close to 0.3, the equilibrium temperature of the Earth in energy balance with the sun would be close to 255 K^{ 4,5}. The corresponding OLR can be computed for MILIA for the U.S. Standard atmosphere, zero GHG, and a temperature offset of -33.2 K so as to drop the surface temperature from 288.2 K to 255 K. The Stefan Boltzmann (S.B.) law yields OLR values of 240 w/m^{2} , 235 w/m^{2} , and 232.8 w/m^{2} for Earth surface thermal emissivity values of 1, 0.98, and 0.971 respectively. The OLR value for the old version of MILIA, which assumed an emissivity of 0.98 and covered a frequency range 100 to 1500 wn, was ** 225** W/m

^{2}. This value differed from the S.B. value of

**W/m**

*235*^{2}by 10 W/m

^{2}. The new version of MILIA, which assumes an emissivity of 0.971 and covers the frequency range 2 to 2200 wn, yields

**W/m**

*232.6*^{2}. This value agrees well with the expected S.B. value of

**w/m**

*232.8*^{2}.

2. In order to elucidate the effect of clouds on the over all OLR, the “cloud free OLR” is an important quantity of research interest. For the MILIA cloud free OLR at 70 km, one simply runs the U.S. Standard Atmosphere with default GHG at 70 km with no clouds or rain. The old version of MILIA yields a value of ** 260** w/m

^{2}. The new version yields

**w/m**

*267*^{2}. The AIRS spectrometer in the Aqua satellite finds a value of

**w/m**

*274*^{2}.

^{6}

3. The MILIA page, that the user opens, has a “Show Raw Model Output” button. The contents revealed by this button comprise approximately 18,000 words, 3,200 lines, and 130,000 characters. This is not the kind of document that the student is likely to open and study on his/her own, although it gives useful information for the serious and persistent user. Instead of looking for the emissivity by using the “Show Raw Model Output” button, it is “reasonable” for a student to proceed as follows: (a) Use the U.S. Standard Atmosphere. (b) Set the observer at zero altitude, looking down. (c) Determine the OLR. (c) Divide the OLR for step c by the OLR expected from the S.B. law, assuming emissivity one and temperature 288.2 K. With the old version of MILIA this procedure results in an apparent emissivity of 0.92, whereas the actual emissivity is 0.98. This error is ~ 6%. With the new version, the same procedure yields 0.976 whereas the actual emissivity assumed by the program is 0.971. The error is reduced in the new version of MILIA to ~ 0.5%.

In regards to items (2) and (3) above, one can show using the atmospheric paths/ radiance feature of SpectralCalc that the OLR for the case of CO_{2} as the only GHG decreases as the emissivity drops. The difference in OLR due to a doubling of CO_{2}^{ } at 10 km was determined using SpectralCalc. This difference in OLR due to doubling the carbon dioxide concentration drops from a value of 4.53 w/m^{2} to 4.15 w/m^{2} linearly as the emissivity drops from 1 to 0.95. However, the scattered IR that tresults from emissivity values less than one compensates for the loss in emitted IR since the scattered radiation is absorbed in the atmosphere by water vapor.^{7}Thus, since neither MILIA nor SpectralCalc take into account radiation scattered from the Earth's surface, values obtained for the loss in OLR due to doubling carbon dioxide concentrations are likely to be artificially decreased the more the emissivity used decreases from one.

References:

- http://www.iapmw.unibe.ch/teaching/vorlesungen/atmosphaerenphysik/FS_2015/Problems5_2015.pdf
- http://faculty.weber.edu/dbedford/classes/geog_1400/1400_lectures.htm
- Derek Wilson and Julio Gea – Banacloche Am. J. Phys. 80, 306 (2012)
- David Archer, “GlobalWarming (Understanding the Forecast)”,Blackwell Publishing, 2007
- Richard Wolfson, “Energy, Environment, and Climate” W.W. Norton, 2008
- Xiuhong Chen, et al, Journal of Climate 26, 478 – 494, table 3.
- Daniel R. Feldman, et al, PNAS, V. 111, 16297 (2014)