The Python data are used to estimate the level of atmospheric fluctuations over 2 months of the summer. The distribution is bimodal, with long periods of very stable conditions (T_rms < 1 mK in a 6° strip) broken by occasional periods of much stronger fluctuations (T_rms < 10 mK), which appear to be associated with clouds. These periods are correlated with a change in wind direction that brings moist air from West Antarctica.
South Pole Atmospheric Fluctuation Data
Altitude of the fluctuations
Comparison with Atacama Desert, Chile
From these data we construct a cumulative distribution function for the brightness fluctuation power, and derive quartiles for brightness fluctuation power over the 2 month time period during which the data were taken. The cumulative distribution function for the data files, in which the covariance has been averaged for only a few minutes, is adequate for deriving the 50% and 75% quartiles. However, instrument noise dominates the distribution function at the 25% quartile level; therefore data that are binned in 6 hour intervals are used to derive the 25% quartile. The quartiles for the 2 months of the austral summer 1996-1997 are 0.20 mK, 0.51 mK and 1.62 mK. To compensate for instrumental filtering effects described above, we increase these values by 30% to 0.27 mK, 0.68 mK, and 2.15 mK. The Python experiment was not operated during the austral winter, so data are not available for this period. However, precipitable water vapor and sky opacity quartiles are lower in the winter months (Chamberlin et al. 1997). It is therefore likely that the atmospheric stability improves during the austral winter as well.
The cumulative distribution function of brightness fluctuation power for the Python data shown in previous figure. Two distributions are shown, one for unbinned data files taken over a few minutes (solid line), and one for the data binned in 6 hour intervals (dash-dot line). The unbinned data files are adequate to determine the 50% and 75% quartiles, but the 6 hour binned cumulative distribution function is needed to achieve adequate signal-to-noise to estimate the 25% quartile. The increased fraction of high fluctuation power data in the 6 hour binned cumulative distribution function results from binning brief periods of high fluctuation power together with periods of low fluctuation power. The quartiles are 0.20, 0.51 and 1.62 mK (before compensating for instrumental effects).
The sharp roll-off of the Python primary beam spatial filter prevents an accurate determination of the underlying atmospheric angular power spectrum. The angular power spectrum for data that have not been tapered at the edges of the sweep exhibits power proportional to the inverse square of the angular wavenumber. This power law dependence is due to power from low angular wavenumbers (large angular scales) leaking into higher angular wavenumber channels. The observations demonstrate that it is desirable to taper CMB data to reduce contamination from the high atmospheric fluctuation power on large angular scales.
a) Time--angle plot for 30 s of Python V data during bad weather, illustrating the striping that results when the wind blows blobs of water vapor along the sweep direction. b) Power spectrum for a 1 hour period which includes the sample shown in (a). Contours are relative to maximum (0.9, 0.8, 0.7, ..., 0.2, 0.1, 0.09, 0.08, etc.). Note that the power is concentrated in a line that is perpendicular to the striping in (a). The radial lines correspond to different altitudes, based on the windspeed measured by radiosonde launches. The y-axis corresponds to ground level, and subsequently shallower lines represent 500, 1000, 1500, 2000, 2500 and 3000 m, respectively. The fluctuations in (a) are at roughly 1500 m above ground. c) Another example showing fluctuations at less than 500~m. d) Two fluctuation components; one very low, the other very high.
By combining the data with radiosonde wind measurements, it is possible to determine the altitude of the fluctuations during periods of bad weather. This is illustrated by the figure above, which shows the measured emission as a function of angular position _x on the sky and time t. The plot represents an interval of 30~s, at a time when the wind was blowing parallel to the sweep direction. The stripes are produced by blobs of water vapor moving from left to right; the diagram shows that a blob moves through an angle of 7° in about 13 s. A 7° angular distance corresponds to a physical length of 0.12 h_av / sin (49°), where h_av is the average altitude of the fluctuation. The radiosonde launched 2 hours after this dataset indicated a fairly uniform wind speed of w = 16 m/s for the lower 2 km, so a blob is expected to move 208 m in 13 s. Solving for h_av gives 1300 m. The slope of the stripes is proportional to h_av/w.
In order to average the data together from many 30-s intervals, we compute the power spectrum for each time--angle plot and average those together. The power spectrum for a 30-s interval is calculated by computing the Fast Fourier Transform of the time--angle data from each of the two horns (using a Hann taper to minimize sidelobes), and then calculating the covariance between the two transformed datasets. Figure b above shows the power spectrum averaged over one hour of data (containing the 30-s interval shown in Fig. a above). The power is distributed along a radial line, perpendicular to the striping. The gradient of this line is proportional to w/h_av; the overlaid radial lines represent (from vertical) altitudes of 0, 500, 1000, 1500, 2000, 2500 and 3000 m, calibrated using w = 16 m/s. The fluctuations have h_av ~ 1300 m. The physical periodicity is given by w/; e.g. = 0.1 Hz corresponds to a fluctuation with period 160 m. There is little power present at the origin because the DC level was removed from the time--angle plane before the Hann taper and Fourier transform were applied. The contours appear to fall off faster than would be expected for Kolmogorov turbulence. This is partly due to the effect of the primary beam taper in the angular wavenumber direction, which can be represented by a Gaussian centered on zero with a FWHM size of about 33 rad, but may also indicate that these bad weather fluctuations do not follow a Kolmogorov power law.
Average power spectra were computed for all the hours when the wind was parallel to the sweep direction (approximately every 12 hours). Two more examples during periods of bad weather are shown in Fig. c and d above. The first indicates fluctuations at an altitude of ~500 m; the second shows two components: one at ~300 m and another at much higher altitude (>3 km). Unfortunately it was not possible to detect structure in the power spectrum during stable periods; the emission is too weak.
In most cases that were measured, the altitude determined for the strong fluctuations, which varies from 300 m to well over 3 km, agreed well with the altitude at which the relative humidity was a maximum (measured by radiosonde launches). This strengthens the case for the connection between clouds and strong fluctuations, and may explain the possible non-Kolmogorov nature of the power spectrum. In the cases of high altitude turbulence (h_av > 3 km), however, there was no corresponding maximum in the relative humidity and there is generally little water vapor present in the atmosphere. Another mechanism must be at work in these cases.
During normal stable conditions the rms brightness temperature variation in a 6° strip was less than 1 mK. It was not possible to determine either the average altitude or the power spectrum of these very weak fluctuations.
The bad weather fluctuations have rms brightness temperature variations of up to 100 mK over a 6° strip of sky, at a frequency of 40 GHz. They are only present when there is at least partial cloud cover. The windspeed as a function of altitude was used to determine the average altitude of the fluctuations. This varied from 500 m to over 4 km, and in most cases corresponded to the altitude at which the relative humidity was a maximum. The power spectrum measured for these bad weather fluctuations appears to fall off faster than the predicted Kolmogorov power law, although this may be due to the taper imposed by the primary beam. We conclude that these strong fluctuations are probably associated in some way with cloud activity.
Path fluctuation data from a satellite phase monitor located in the Atacama Desert in Chile were used to estimate the corresponding level of brightness temperature fluctuations at 40 GHz for that site. Although this conversion is uncertain by a factor of 2, and the result depends strongly on the unknown altitude of the turbulent layer, the two months of South Pole data indicate a significantly lower level of fluctuations compared to the Chile site, as shown in the table above.
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