## Atmospheric emission and attenuation

As stated earlier, the main absorptive constituents of the atmosphere are oxygen and water vapour, each of which have absorption bands in the millimeter and submillimeter wavelength region. Considerable effort has been devoted to constructing a propagation model of the atmosphere and to derive the resulting absorption as function of frequency. Major contributions are due to Liebe (1989) and also Pardo et al. (2001) for the submillimeter wavelength region. While the oxygen contribution is rather constant and similar over the world, the contribution of water vapour is highly dependent on the local weather situation. Generally the models assume an exponential decrease of the oxygen and water vapour concentration with height. The scale height is defined as the height where the concentration has decreased to a value 1/e = 0.37 of the surface value. For oxygen the scale height is typically 8 km, while that of water vapour is about 2 km. Thus it is clear that a significant decrease in the influence of water vapour can be achieved by locating the telescope on a high and dry site. This has indeed been done with most dedicated millimeter telescopes.

The zenith attenuation (often called opacity from the usage in optical astronomy) as shown in Fig. 6.19 is connected to the atmospheric self-radiation through Kirchhoffs Law. If we denote the zenith opacity by t0 we can write for the antenna temperature at the antenna terminals

where TA (0) is the antenna temperature at the top of the atmosphere and Tatm the effective temperature of the atmosphere. The zenith opacity t0 will vary according to the changes in the water vapour density and must normally be measured at regular intervals. This is often done by performing a "tipping scan" measurement, whereby the opacity is determined from the antenna temperature as measured over a large zenith angle range (without background sources). The air mass matm(the total column mass of the atmosphere), defined to be unity towards the zenith, increases to a first approximation as the secans of the zenith angle, whereby the atmosphere is considered as a set of plane parallel sheets. For large zenith angles a more accurate formula might be needed, whereby the curvature of the atmospheric layers is taken into account. Rohlfs and Wilson (1996) give a power series, valid to 4 air masses (zenith angle of 75 degrees) with an error of less than 1 percent, of the form matm(z) = -0.0045 + 1.00672 sec z - 0.002234 sec2 z - 0.0006247 sec3 z . (6.21)

Performing a tipping scan, we easily see from Eq. (6.20) that the measured antenna temperature as function of the zenith angle z will be

Plotting the logarithm of the measured signal against sec z (the air mass along the line of sight) delivers the zenith opacity from the slope of the curve. Care should be taken that the measurement is not corrupted by varying radiation received in the sidelobes of the antenna, which will pick up significant amounts of ground radiation for large zenith angles. For this reason the scan is normally stopped at about 70 degrees zenith angle. The opacity can also be found from the change in measured antenna temperature from a sufficiently strong radio source as function of zenith angle. In this case we must however assume that the atmospheric opacity is constant over the long duration of the measurement, because the zenith distance varies by no more than 15 degrees in one hour. Therefore, the tipping scan has been adopted at many observatories as a routine method to quickly determine the atmospheric opacity.

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