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 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.
Figure 7: a-h) Phase power plots and 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
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
The data are processed in 24 hours periods. There are several steps involved.
First of all, phase wraps and 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
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 . In practice only the lowest two frequencies (0.0 Hz and
Hz) are reduced significantly.
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.
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
(equivalent to 110
m of path). The
plot shows the signature expected from atmospheric phase noise; the straight lines have gradients of
and
. 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
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.
The data of Figs. 7b and d correspond to an integrated rms phase
of at 12 GHz (170
m of path).
The
plot again shows the characteristic signature of the
atmosphere and the contribution from instrumental noise
for
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
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.
Figure 8: Data for Feb. 4 1995 with five model curves superimposed.
The solid, long dash, short dash and dotted lines have 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
of 1 km, but with the wind blowing parallel to a 100 m baseline. All models are for an elevation of 45
, 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 in the range 100 to 1000 m. The shape of the curve for
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
m s
, or 9 mph.
Since the elevation is
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
5 mph.
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 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 s
or 5 mph, requiring a 7 mph wind perpendicular to the baseline, compared to the recorded value of
4 mph at ground-level. There is still substantial phase power on timescales of 1000 s or more.
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 and there is a more marked
discontinuity in the gradients of the
plot. The integrated rms phase at 12 GHz is
, corresponding to 360
m 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 and dominates for
; the second has a maximum at
, similar to the example in panel b. To account for the sharp change in gradient of the
plot
and the steep curve at
in the spectral
density plot, the wind for the high frequency component must be approximately
parallel to the baseline at
m s
(50 mph). The second component has a projected windspeed of
9 mph, as for the example of Feb. 4 1995.