Skydips

The skydip observing mode measures the sky brightness at a range of elevations and uses that data to calculate the zenith sky opacity. The absolute value of the sky brightness is required and this values is calculated by interpolating its measured signal from that measured with ambient and cold loads.

In order to calculate the zenith sky opacity to the sky brightnesses the skydip task fits a theoretical curve to the data. The theoretical curve at each wavelength takes the form:

$$J_\mathrm{meas} = (1 - \eta_\mathrm{tel}) J_\mathrm{tel} + ... ...\mathrm{atm} - b \eta_\mathrm{tel} J_\mathrm{atm} e^{-A\tau},$$ (3)

where $J_\mathrm{meas}$ is the measured brightness temperature of the sky, $\eta_\mathrm{tel}$ is the transmission of the telescope, $J_\mathrm{tel}$ is the brightness temperature of a black-body at the temperature of the telescope, $J_\mathrm{atm}$ is the brightness temperature of the atmosphere, $b$ is the bandwidth factor of the filter being used ($1-b$ is the fraction of the filter bandwidth that is opaque due to atmospheric absorption and, like $\tau$, it is a function of water vapour content), $\tau$ is the zenith sky optical depth and $A$ is the airmass of the measurement.

Of these parameters, $J_\mathrm{meas}$, $J_\mathrm{tel}$ and $A$ are known. $J_\mathrm{atm}$ can be estimated from the ambient air temperature at ground level using a model for the behaviour of the observing layer above the telescope, as described below. $\eta_\mathrm{tel}$ may be fitted to the data for every skydip and, because it does not vary with atmospheric conditions, a reliable `average' value can be derived from many observations. Thus, there are two remaining free parameters, $\tau$ and $b$, that must be derived from the fit (three if fitting $\eta_\mathrm{tel}$).

$J_\mathrm{atm}$ is calculated from $T_\mathrm{amb}$, the ambient air temperature, by assuming that the sky emission is dominated by a single absorber/emitter whose density falls exponentially and temperature linearly with height. In this case it can be shown that

$$J_\mathrm{atm} = J_\mathrm{amb} \int_0^{40}\! A \left[k\exp\... ...\right)\right] \left(1-\frac{h}{h_1}\right)\right]\mathrm{d}h,$$ (4)

where $h_1$ is $J_\mathrm{amb}/6.5$ to give a 6.5 K fall in temperature per km height, $h_2$ is the scale height of the absorbers (2 km), $A$ is the airmass and $k$ the extinction per km.

If we approximate the result of the integral by

$$J_\mathrm{atm} = J_\mathrm{amb} X_\mathrm{g} \left[1-\exp\left(-A k h_2\right)\right],$$ (5)

it can be shown that $X_\mathrm{g}$ has the form

$$X_\mathrm{g} = 1 + \frac{h_2 T_\mathrm{lapse}}{T_\mathrm{amb}}\exp\left(-\frac{A \tau}{X_\mathrm{gconst}}\right)$$ (6)

where $T_\mathrm{lapse}$ is the temperature drop per kilometre altitude ($-6.5$ K/km) and $X_\mathrm{gconst}$ is a constant determined empirically and has a value of 3.669383.

For more information see [35].