# 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! :) – Jean-Marie Prival Feb 6 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:

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