^{1,2}MILIA, in use since 1995, is the only free online source of OLR data that is available; therefore, it has been used as a test of a simple model for the CO

_{2}no - feedback climate sensitivity.

^{3 }

Until May of 2017, the MILIA web site had an underlying Planck Function which spanned a limited range of wave numbers between 100 wn and 1500 wn. The new version described here extends the range of the underlying Planck distribution to 2 wn – 2200 wn.

Fig. 1, at the end of this write-up, shows a comparison between the old version of MILIA and the new version. Fig. 1 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, Stratospheric Ozone scale 1, and water vapor scale 1. The left side image represents MILIA before May 2017; the right side represents the newer version, online after May 11, 2017.

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

- A common derivation in basic environmental Physics text books results in the following important result: If there were no Greenhouse Effect, and albedo of close to 0.3, the net solar flux onto the Earth would be 239 w/m
^{2}. Assuming the emissivity of the Earth in the thermal IR is unity, the temperature of the Earth in energy balance with the sun would be 255 K.^{ 4,5}For ε of 0.98, corresponding to the old version of MILIA, the thermal OLR would be comprised of 2% scattered radiation, but the radiant emission in the IR would be 235 W/m^{2}. For U.S. Standard atmosphere, zero GHG, and a temperature offset chosen to drop the surface temperature from 288.2 K to 255 K, the old version of MILIA yields an OLR value of 225 w/m^{2}as opposed to the correct value of 235 w/m^{2}.*The resulting relative error is ~ 4%.*For the new version of MILIA, with emissivity in the thermal IR of 0.97, the correct value of the OLR is 232.5 K and the value of radiant OLR from MILIA is 232.6 w/m^{2}. The*relative error is now ~ 0.04%.* - In order to elucidate the effect of clouds on the overall OLR, the “cloud free OLR” has become a quantity of research interest. To obtain 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
w/m*260*^{2}. The new version yieldsw/m*267*^{2}. The AIRS spectrometer in the Aqua satellite^{6}finds a value ofw/m*274*^{2 }. - The MILIA page exhibits a “Show Raw Model Output” button. The corresponding document contains 18,000 words and Is not the kind of thing that the student is likely to open and study on his/her own, but it gives useful information for the persistent user. Instead of looking up the value of the emissivity ε by using the “Show Raw Model Output” button, it might seem “reasonable” to the user to proceed as follows: (a) Use the U.S. Standard Atmosphere. (b) Choose zero altitude and determine the OLR. (c) Divide this OLR by the OLR expected from the S.B. law, assuming (ε, temp) values of (1, 288.2 K). With the old version of MILIA such a procedure results in ε = 0.92, whereas the actual emissivity is 0.98; the resulting relative error is ~ 6%. With the new version, the relative error introduced by the procedure is reduced by an order of magnitude.

We also note that if ε decreases to values increasingly smaller than one, the radiated OLR decreases accordingly but the compensating scattered radiation increases. Except for certain arid regions, most scattered thermal IR is absorbed by water vapor.^{7 }Neither MILIA (nor SpectralCalc) takes into account radiation scattered from the Earth's surface. Therefore, values obtained by MILIA for the OLR will decrease as ε decreases. To quantify this effect, the loss in radiant OLR at 10 km, due to doubling the CO2 concentration, was calculated using SpectralCalc. The value of ΔF so calculated decreases in going from ε = 1 to ε = 0.97 by only 5%. This error would increase to 13% if a user were to mistakenly use ε = 0.92, but such a mistake is impossible using the new version of MILIA.

Other updates are the introduction of a button for the Freon concentration and an improved presentation of the altitude versus temperature plots in cases of non-zero temperature offset. The problem of displaying accurate temperature versus altitude plots in cases of large offset is complex, and is difficult to do accurately in an application such as MILIA. Perhaps better temperature versus altitude plots could be another improvement at a future time.

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, “Global Warming (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)