The Earth atmosphere

While our atmosphere is quite transparent for radio waves, its influence is not negligible: Its presence causes additional noise - from its thermal radiation - and at higher frequencies an attenuation of celestial signal - from absorption by air molecules. Since a line-of-sight at low elevation passes through a longer column of air than when looking at the zenith, these effects increase towards lower elevations. If one measures the radiation from the 'empty' sky on 1.3 GHz at various heights above the horizon, one obtains a series of steps:

The additional increase of noise above about 70º is due to the antenna spill-over (cf. there). Apart from this effect, the systematic increase of the noise level towards the horizon can be explained quantitatively in the following way: Since the denser atmospheric layers - the troposphere - constitute a layer up to about 8 km above the ground, one can neglect their thickness in comparison with the Earth radius and represent them as a plane-parallel layer. If L is the air column encountered while looking towards the zenith, the column towards elevation ε will be larger: L/sin ε. A plot of the measurements taken at various elevations against 1/sin ε shows a straight-line relation:

The values in parentheses are not taken into account, due to spill-over and pick-up of ground radiation at 15º.

Interpretation of the data

is based on the sketch of the principles:

Red squares represent measured data, the blue dots mark points that are extrapolated from the data. The measured signal is composed of several constituents:

Matching the data with a straight line results in the line slope m and the Y-axis offset b, the value at 1/sin ε=0. This value is not represented by any real elevation angle, but one would obtain this extrapolated value in the absence of the Earth atmosphere!

The data are a measure of the power received by the antenna, but expressed in some arbitrary units, determined by the apparatus. If these are given in dB (deciBel), they need to be converted in linear powers (p = 10dB/10). In order to convert the raw values into antenna temperatures, we need to determine the scale factor a:

p(source) = a (Tsource + Tsky(ε) + Tsys + TCMB)
which includes all contributions from the source, the atmosphere, the receiver, and the microwave background. To resolve this, we execute a flux calibration: the antenna is pointed to the ground, a building, or - as with the 1 GHz antenna - a nearby dense grove of trees, which fills the antenna beam completely with its thermal radiation (at Tcal = 290 K):
p(cal) = a (Tcal + Tsys)
Since we do not point to the sky, there are no contributions from atmosphere and CMB. From the sketch one recognizes that
b = a (Tsys + TCMB)
Hence the scalenfactor is
a = (p(cal) - b) /(Tcal - TCMB)
and one obtains the system temperature:
Tsys = b(Tcal - TCMB)/(p(cal) - b) - TCMB
Finally, from p(zenith) = m + b = aTzenith + b one gets from the slope the antenna temperature at the zenith
Tzenith = m/a = m(Tcal - TCMB)/(p(cal) - b)

Results

For 1.4 GHz one obtains a zenith temperature of about 5 K, which appears to be quite independent of the weather.

Measurements on 24 GHz give zenith temperatures of 20..30 K. It is remarkable that the measured values do not lie on a straight line, but rather on a curved relation. This is due to atmospheric attenuation by water vapour in the air. This is currently being studied in more detail (Oct. 2014) ...


Weather

Last but not least, there is the weather: passing rain clouds and showers may produce enhanced noise due to thermal radiation by water vapour and rain drops. Here is an example from 24 GHz of a couple of rather substantial autumn showers: