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3. Observations

3.1. The instrument

The data presented here are from the atmospheric phase monitor at the Owens Valley Radio Observatory. This instrument comprises two 1.2 m off-axis antennas separated by an East-West baseline of 100 m. The design is based on the system built by Masson et al. (1990), and is on loan from the Center for Astrophysics. The antennas are directed at a geosynchronous communications satellite in the South at an elevation of tex2html_wrap_inline1631 that emits an unmodulated tone at 11.7 GHz. The signals are down-converted and the phase difference between them is measured with a vector voltmeter and recorded every second. The phase difference varies with time as a result of turbulence in the atmosphere, drifts in the instrument response, and motions of the satellite along the line of sight. A dedicated phase monitor of this type provides a continuous record of the state of the atmosphere in a fixed direction on the sky, whereas measurements derived from bright astronomical sources are usually over only a limited period of time dictated by the observing schedule.

  figure408
Figure 7: a-h) Phase power plots and tex2html_wrap_inline1633 plots for 4 days in the Owens Valley. a) and c) are for Oct. 25 1995, and illustrate a very calm atmosphere, setting upper limits on the instrumental contributions; b) and d) are for Feb. 4 1995 showing typical conditions; e) and g) are for Feb. 5 1995 which show that there can be substantial power on long timescales; f) and h) are for Jan. 12 1995 and show substantial power on short timescales, probably with two components. All but the last dataset have the same vertical scales. The lines on the tex2html_wrap_inline1635 plots have gradients of -8/3 and -2/3, as predicted for a very thick layer of Kolmogorov turbulence, but no formal fitting has been made

3.2. Data processing

The data are processed in 24 hours periods. There are several steps involved. First of all, phase wraps and tex2html_wrap_inline1641 phase jumps are removed. 12- and 24-hour sinusoids are then fitted to and subtracted from the data. This removes almost all of the satellite's radial motion. The data are then divided into segments of 4096 seconds (1 hour and 8 minutes). A straight line is fitted to and subtracted from each segment to remove drifts in the instrument and residual satellite motion, followed by a Fast Fourier Transform to generate 2048 complex values. The power spectrum is then given by the square of the amplitude of these values, and comprises 2048 measurements ranging in frequency from 0.5 Hz to 0.0 Hz, spaced by tex2html_wrap_inline1643 Hz. Finally, the 20 or so power spectra generated for a 24 hour period are averaged together to produce the overall power spectrum for the day. The average rms phase, summed over all timescales up to 4096 s, is also calculated.

The subtraction of a straight line from each segment changes the measured power spectrum. However the impact is minimal, since only the sine terms generated by the Fourier Transform are affected (the cosines are even functions with a first order moment of zero) and the power removed falls off as tex2html_wrap_inline1645. In practice only the lowest two frequencies (0.0 Hz and tex2html_wrap_inline1647 Hz) are reduced significantly.

3.3. The data

The 4 data sets shown in Fig. 7 have been chosen to illustrate different conditions. These are discussed in the next section. Only a limited number of data sets have been examined so far. Each of the four days of data is examined in turn and relevant issues are discussed.

3.3.1. Oct. 25 1995

The data of Figs. 7a and c are for one of the best days for which data is available. The rms phase on the 100 m baseline at 12 GHz, integrated over all timescales up to 4096 s, is tex2html_wrap_inline1649 (equivalent to 110 tex2html_wrap_inline1651m of path). The tex2html_wrap_inline1653 plot shows the signature expected from atmospheric phase noise; the straight lines have gradients of tex2html_wrap_inline1655 and tex2html_wrap_inline1657. There has been no attempt to make a formal fit to the data and the straight lines are shown for illustration only. The instrumental noise becomes apparent for frequencies exceeding tex2html_wrap_inline1659 Hz. The two peaks in the spectral density plot may be due to two distinct components of turbulence moving at different speeds in the atmosphere. The main purpose of showing this dataset is to set an upper limit on the contributions from instrumental noise and satellite motion.

3.3.2. Feb. 4 1995

The data of Figs. 7b and d correspond to an integrated rms phase of tex2html_wrap_inline1661 at 12 GHz (170 tex2html_wrap_inline1663m of path). The tex2html_wrap_inline1665 plot again shows the characteristic signature of the atmosphere and the contribution from instrumental noise for tex2html_wrap_inline1667 Hz. The data are more consistent with the models of Figs. 4d and f, where the wind is perpendicular to the baseline, than with c and e, where the wind blows along the baseline direction. The tex2html_wrap_inline1669 plot shows a more gradual transition between the two gradients than the data shown in Fig. 7h where the wind is most likely along the baseline.

  figure435
Figure 8: Data for Feb. 4 1995 with five model curves superimposed. The solid, long dash, short dash and dotted lines have tex2html_wrap_inline1671 of 100 km, 5 km, 1 km and 100 m, respectively, all with the wind perpendicular to a 100 m baseline. The dash-dot line has a tex2html_wrap_inline1673 of 1 km, but with the wind blowing parallel to a 100 m baseline. All models are for an elevation of 45tex2html_wrap_inline1675, appropriate for the Owens Valley phase monitor

Figure 8 (click here) shows five model curves superimposed on the data. No formal fit has been made, but it is clear that the data are best fitted by tex2html_wrap_inline1677 in the range 100 to 1000 m. The shape of the curve for tex2html_wrap_inline1679 is well-constrained by the data points and is fitted much better with the wind perpendicular to the baseline than along it. The projected windspeed required to map the spatial frequency scale of the model (wind perpendicular to baseline) to the temporal frequencies of the data is tex2html_wrap_inline1681 m stex2html_wrap_inline1683, or 9 mph. Since the elevation is tex2html_wrap_inline1685 in the direction of the wind, the actual windspeed needed to give a projected value of 9 mph is 13 mph. The windspeed recorded at ground-level for that period was tex2html_wrap_inline16875 mph.

3.3.3. Feb. 5 1995

Panels e and f of Fig. 7 show data for the following day. The conditions appear to be similar to Feb. 4 1995 (the integrated rms phase is again tex2html_wrap_inline1689 at 12 GHz), except that the data are shifted to lower frequencies, indicative of a lower windspeed. The projected windspeed obtained is 2.5 m stex2html_wrap_inline1691 or 5 mph, requiring a 7 mph wind perpendicular to the baseline, compared to the recorded value of tex2html_wrap_inline16934 mph at ground-level. There is still substantial phase power on timescales of 1000 s or more.

3.3.4. Jan. 12 1995

The data in panels f and h are clearly different in character from the preceding examples. There is substantial phase power on timescales as short as 10 s. The data rise very rapidly from high tex2html_wrap_inline1695 and there is a more marked discontinuity in the gradients of the tex2html_wrap_inline1697 plot. The integrated rms phase at 12 GHz is tex2html_wrap_inline1699, corresponding to 360 tex2html_wrap_inline1701m of path (note the different scaling on the spectral density plot).

The shape of the distribution in Fig. 7f can only be reconciled with the model if there are two components of turbulence present, moving at different speeds. One has a maximum centered on tex2html_wrap_inline1703 and dominates for tex2html_wrap_inline1705; the second has a maximum at tex2html_wrap_inline1707, similar to the example in panel b. To account for the sharp change in gradient of the tex2html_wrap_inline1709 plot and the steep curve at tex2html_wrap_inline1711 in the spectral density plot, the wind for the high frequency component must be approximately parallel to the baseline at tex2html_wrap_inline1713 m stex2html_wrap_inline1715 (50 mph). The second component has a projected windspeed of tex2html_wrap_inline17179 mph, as for the example of Feb. 4 1995.


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