Infrared and Sub-millimetre Observing Conditions on the Antarctic Plateau

Marton G. Hidas, Michael G. Burton, Matthew A. Chamberlain, John W.V. Storey, PASA, 17 (3), 260.
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The effect of water content

The starting point for the following analysis is the model shown in Fig. 1, obtained from radiosonde data taken on a clear day. The total precipitable water vapour for this model is 164$\mu$m, which is close to the lowest value measured at the South Pole during winter (Van Allen et al. 1996). This model did not include any aerosols.

The spectrum was calculated for the original model, as well as for two variations, one with the relative humidity at each layer of the atmosphere in the model doubled, and another with the relative humidity halved. The resulting emission and transmission spectra are shown in Figures 3-6, for the wavelength ranges 2-6$\mu$m, 5-15$\mu$m, 15-60$\mu$m and 50-500$\mu$m, respectively. Table 2 and Table 3 give some numerical values for the sky flux and transmission, averaged over several wavelength regions of interest.

Table: Model sky fluxes (in Jyarcsecond^-2) averaged over various spectral regions, showing the effects of varying precipitable water vapour content and aerosol visibility

Wavelength	Precipitable Water Vapour / Aerosol Visibility
Range ($\mu$m)	($\mu$m) / (km)
	164 / $\infty$	82 / $\infty$	324 / $\infty$	164 / 100	164 / 10	164 / 1
3.0-3.1	2.2 x 10-3	1.3 x 10-3	3.6 x 10-3	3.1 x 10-3	1.4 x 10-2	3.3 x 10-2
3.6-3.8	7.0 x 10-3	6.5 x 10-3	8.0 x 10-3	2.9 x 10-2	3.0 x 10-1	6.5 x 10-1
3.0-4.0	2.1 x 10-2	2.0 x 10-2	2.2 x 10-2	3.3 x 10-2	2.0 x 10-1	4.2 x 10-1
4.9-5.1	1.2 x 100	8.3 x 10-1	1.8 x 100	1.7 x 100	8.1 x 100	2.2 x 101
8.2-9.2	2.5 x 101	2.4 x 101	2.7 x 101	3.3 x 101	1.3 x 102	6.2 x 102
10.2-11.2	1.3 x 101	1.3 x 101	1.3 x 101	2.2 x 101	1.6 x 102	9.5 x 102
10.0-13.0	2.5 x 101	2.4 x 101	2.7 x 101	4.3 x 101	2.5 x 102	1.4 x 103
18.0-22.0	5.5 x 102	3.8 x 102	8.0 x 102	6.0 x 102	1.2 x 103	3.8 x 103
20.0-20.2	8.1 x 101	4.1 x 101	1.6 x 102	1.3 x 102	7.7 x 102	3.7 x 103
24.1-24.9	4.3 x 102	2.2 x 102	8.0 x 102	4.6 x 102	9.1 x 102	3.3 x 103
32.0-32.5	2.4 x 103	1.5 x 103	3.5 x 103	2.4 x 103	2.6 x 103	3.4 x 103
220-230	2.0 x 102	1.5 x 102	2.4 x 102	2.0 x 102	2.0 x 102	2.0 x 102
330-370	4.9 x 101	3.8 x 101	6.6 x 101	4.9 x 101	4.9 x 101	5.1 x 101
430-470	2.7 x 101	2.0 x 101	3.8 x 101	2.7 x 101	2.7 x 101	2.8 x 101

Table: Model atmospheric transmission, averaged over various spectral regions, showing the effects of varying precipitable water vapour content and aerosol visibility

Wavelength	Precipitable Water Vapour / Aerosol Visibility
Range ($\mu$m)	($\mu$m) / (km)
	164 / $\infty$	82 / $\infty$	324 / $\infty$	164 / 100	164 / 10	164 / 1
3.0-3.1	0.94	0.96	0.90	0.92	0.67	0.05
3.6-3.8	0.98	0.98	0.98	0.96	0.64	0.03
3.0-4.0	0.91	0.92	0.89	0.88	0.61	0.03
4.9-5.1	0.95	0.96	0.93	0.93	0.70	0.07
8.2-9.2	0.96	0.96	0.96	0.95	0.86	0.38
10.2-11.2	0.99	0.99	0.99	0.99	0.93	0.56
10.0-13.0	0.99	0.99	0.98	0.98	0.90	0.47
18.0-22.0	0.89	0.93	0.85	0.89	0.77	0.27
20.0-20.2	0.98	0.99	0.97	0.98	0.85	0.30
24.1-24.9	0.92	0.96	0.85	0.91	0.83	0.38
32.0-32.5	0.48	0.67	0.24	0.47	0.44	0.27
220-230	0.21	0.39	0.07	0.21	0.21	0.20
330-370	0.56	0.66	0.41	0.56	0.56	0.54
430-470	0.61	0.71	0.46	0.61	0.61	0.60

MODTRAN calculates the total vapour column of absorption, h, for a species such as water, as

$$h = \frac{1}{\rho_0 R m_a} \int {U r_w(P,T) \frac{P}{T} dz},$$ (1)

where U is the relative humidity, P and T the pressure and temperature of the air, and r_w the saturation mixing ratio of moist air (ie the mass of water in saturated air compared to the equivalent mass of dry air that contains it), all functions of z, the height. $\rho_0$ is the density of dry air at STP, m_a the molecular mass of air and R is the gas constant. The column, h, can also be related to the precipitable water vapour content, X, by

$$h = \frac{\rho_w m_a}{\rho_0 m_w} X$$ (2)

or h (cm) = 0.12 X ($\mu$m), where $\rho_{w}$ is the density of liquid water at STP and m_w its molecular mass (g/mole).

Note that part of the reason for the low water vapour content of the atmosphere above Antarctica is that, at these low temperatures, the saturation vapour pressure of water is low. For instance, while r_w is 8g/kg at 10$^{\circ}$C and 1,000mbars it is only 0.2g/kg at $-40^{\circ}$C and 600mbars. Therefore, even when the relative humidity is close to 100%, the actual amount of water vapour is still small. When the relative humidity profile of the original model was doubled, it actually exceeded 100% at one level, and had to be reset to 100%. This is why the ``wet'' case does not have exactly twice the precipitable water. In fact, even scaling the relative humidity up by an unphysical factor of 10 only resulted in 540$\mu$m of precipitable water.

Halving and doubling the humidity this way encompasses the range of precipitable water vapour content encountered at the South Pole. For instance, Chamberlin, Lane & Stark (1997) show that in winter there is less than 190$\mu$m of precipitable water vapour for 25% of the time, and less than 320$\mu$m for 75% of the time. Even in summer the column is less than 470$\mu$m for half the time. Furthermore, the precise determination of water vapour content from radio-sonde data is difficult below $-40^{\circ}$C (eg. see Walden, Warren & Murcray, 1998), and so encompassing the likely range this way allows more robust conclusions to be drawn than by detailed modelling of several sets of radio-sonde data.

Figure 3: Comparison of emission and transmission spectra with varying water vapour content in the near-IR, from 2 to 6$\mu$m. The solid line is the spectrum for the original model (profiles shown in Figure 1), with total precipitable water content 164$\mu$m. The dashed line (upper curve on the emission spectrum, lower curve on the transmission spectrum) is the same model, but with almost double the water content (324$\mu$m), while the dotted line (lower and upper curves, respectively) is for when the water vapour content is halved (82$\mu$m).

Figure 4: Comparison of emission and transmission spectra with varying water vapour content in the mid-IR, from 5 to 15$\mu$m, as for Fig. 3. Note that the flux range is different.

Figure 5: Comparison of emission and transmission spectra with varying water vapour content in the mid-IR, from 15 to 60$\mu$m, as for Fig. 3. Note that the flux range is different.

Figure 6: Comparison of emission and transmission spectra with varying water vapour content in the far-IR and sub-mm, from 50 to 500$\mu$m, as for Fig. 3. Note that both the flux range and the transmission range are different.

From 2-15$\mu$m there is relatively little variation in either transmission or flux as the water vapour content is varied (except within the water absorption band itself around 6$\mu$m). It seems, therefore, that at a very dry site such as the Antarctic plateau, the exact value of the water content is not an important factor in determining the observing conditions in the dark regions of the near- and mid-IR spectrum.

For wavelengths beyond 20$\mu$m, however, it is a different story. The opening of the mid-IR window at 30$\mu$m is critically dependent on low levels of water vapour, being effectively closed for 324$\mu$m of precipitable water vapour. While the background fluxes do not vary significantly with water vapour content, the transmission, and thus ability to detect a signal, does. In particular, the new far-IR windows at 200$\mu$m and 230$\mu$m do require the driest days for successful observing. However the only terrestrial locations from which these windows are accessible at all are probably those on the Antarctic plateau.

Next Section: The effect of aerosols
Title/Abstract Page: Infrared and Sub-millimetre Observing
Previous Section: The effect of temperature
Contents Page: Volume 17, Number 3