How does Earth's thermal radiation into space vary by location and time of day?

CHEOPS (also 1, 2, 3) is a space telescope recently put in low Earth orbit to look for exoplanets around other stars. It uses a cooled detector array and so uses a heat shield to avoid thermal radiation from the Sun as well as the Earth directly below.

Thermal radiation from the Earth is a significant problem for spacecraft thermal management in low Earth orbit, so it's important to know how much thermal radiation Earth emits into space.

If we use an average emissivity $$\epsilon$$ of 0.8 and assume a temperature of 0 °C, then using

$$P= \sigma \epsilon T^4$$

where the Stefan-Boltzmann constant $$\sigma$$ is 5.67 $$\times 10^{-8}$$ W m-2 K-4 we can estimate it to be about 250 W/m2.

But what is it really, and how does it vary (on average) by the type of terrain under a satellite and time of day?

From this answer to For a given 48 hour observing period, what fraction of the celestial sphere is available to CHEOPS? (originally from the CHEOPS Red Book ESA/SRE(2013)7 November 2013 • When I think of "local variations of Earth's thermal radiation", I always think of this map: en.wikipedia.org/wiki/Earth%27s_internal_heat_budget#/media/… Then I realise Earth's internal heat is nothing compared to the solar contribution (we're talking mW/m$^2$ here)... But as a solid Earth scientist I couldn't help myself to post it anyway! :) Feb 6 '20 at 10:01

The yearly average Top Of Atmosphere (TOA) Outgoing Longwave Radiation (OLR) is around 145–345 W/m², as measured by the AIRS instrument: Source: Wikimedia Commons contributors, "File:AIRS OLR.png," Wikimedia Commons, the free media repository.

Now, this is an average that includes both day and night. How much does it vary? This depends on the location. Based on GERB data, a 2007 paper estimates (please pay attention to the thick solid line only): Source: Comer, Slingo, and Allan (2007)

Even in places with a very large diurnal temperature cycle such as the Sahara, the difference between maximum and minimum is only about 10%. In oceanic areas it is closer to 2%. That means that if you take the mean (shown in the top figure) and subtract around 1–5% depending on the region (the drier, the more difference) you get a reasonable estimate of the nighttime outgoing longwave radiation.

If you want a more precise estimate, you can always download satellite data and calculate it yourself.

Full source for second figure: Comer, Slingo, and Allan (2007), Observations of the diurnal cycle of outgoing longwave radiation from the Geostationary Earth Radiation Budget instrument, Geophysical Research Letters, Vol. 34, L02823, doi:10.1029/2006GL028229