Return to Memolist
MMA Memo 159: Wind Velocities at the Chajnantor and Mauna Kea
Sites and the Effect on MMA Pointing
M.A. Holdaway, S.M. Foster, Darrel Emerson, Jingquan Cheng,
and Fred Schwab
National Radio Astronomy Observatory
email: (mholdawa, sfoster, demerson, jcheng, fschwab)@nrao.edu
August 9, 1996
Abstract:
We analyze wind statistics on the Mauna Kea/VLBA and Chajnantor,
Chile sites for the one year period from May 1995 through April 1996
for the purposes of understanding the effects of the winds on pointing
errors. Both the Chilean and the Mauna Kea sites display seasonal
changes in the wind speed, with winds blowing strongest during the
local winter. There is a very weak diurnal variation of wind speed on
Mauna Kea, and a very strong diurnal variation of wind speed on the
Chilean site with day time winds typically being 2-3 times higher than
the night time winds. Since the opacity and phase stability on the
Chilean site also settle down to their best values at night, high
frequency observations and many of the most demanding mosaics will be
performed at night. Median night time winds on the Chilean site are a
benign 3.5 m/s, lower than the Mauna Kea night time median of 4.2 m/s.
From model distributions of observed AZ and EL and the pointing error
calculations of Cheng (1996, in preparation), we calculate 9 m/s
winds typically produce 3.5 arcsecond pointing errors in the
conventional design antenna. Although Chilean winds are often high,
they are often not highly variable over 10 minutes. The wind power
spectrum in Chile is flatter than the Davenport spectrum (1962). If
pointing is calibrated every 10 minutes, wind induced pointing errors
are reduced to 0.25 - 0.5 of the static wind pointing error, bringing
the conventional antenna close to meeting the pointing specification
of 1 arcsecond or better in the best half of the wind conditions.
In contrast, the slant-axis mount with an on-axis paraboloid (Cheng,
1993) is able to point to 1.3 arcseconds in 9 m/s winds (Cheng, 1996).
The MMA's 1 arcsecond pointing spec is extremely important for
mosaicing at millimeter wavelengths and all observations in the
submillimeter. We need to scrutinize antenna pointing and calibration
in the future to ensure that the MMA antennas will be able to meet
this pointing specification. If it is not believed that the
conventional antenna can get close to the pointing spec, the
slant-axis antenna must be reconsidered.
While the Chilean site has displayed spectacularly good opacity
( 
3 times better than Mauna Kea) and phase stability ( 2
times better than Mauna Kea), the wind statistics have been
troublesome to the engineers. Winds are worst in the months with the
best opacities and phase stabilities, with medians as high as 9 m/s
for the winter months. High winds will affect the MMA antenna's
ability to point accurately. Originally, the MMA antennas were given
a pointing specification of 1 arcsecond rms to enable the MMA to make
high quality mosaic images (Cornwell, Holdaway, and Uson, 1994). It
was realized later that the 1 arcsecond pointing specification could
not be met in high winds, and the current specification is to point to
1 arcsecond rms in median winds (Napier et al., 1995). However,
now that the scope of the MMA project has grown to include frequencies
possibly as high as 850 GHz, the 1 arcsecond pointing specification is
even more crucial. Can the MMA antennas point to 1 arcsecond in
Chajnantor's high winds?
Mauna Kea is known for its calm winds, typically 5 m/s. Chajnantor
has seen some very windy conditions, and the median wind speed of
9 m/s for July, 1995 is well known in MMA circles. We recorded the
wind speed and direction about once every 10 minutes at the Chile and
Mauna Kea/VLBA sites as part of our site testing campaign, and a
careful look at the data for a one year period from May 1995 to April
1996 indicates that the Chilean site is not all that windy.
Figures 1 and 2 show the seasonal
variations in the first, second, and third quartile wind velocities at
the Mauna Kea/VLBA and the Chilean sites. Mauna Kea winds are higher
for two months in the local winter, but the Chilean site has high
winds for five months in the local winter. The overall median winds
are 4.5 m/s for Mauna Kea and 6.0 m/s for Chile.
Figure 3 illustrates the lack of diurnal variations in
wind speed on Mauna Kea, and Figure 4 shows the strong
diurnal effect on the Chilean site. The day time winds in Chile are
quite high, but the median night time winds are about 3.5 m/s, which
is lower than on Mauna Kea. This is significant, because both sites
usually experience worse phase fluctuations and opacities during the
day. The approximate peak to peak magnitudes of the diurnal effects
of wind, phase stability, and opacity are summarized in Table 1.
During the night when the best phase stabilities and opacities occur
at Chile, the winds are also quite calm. We will still be able to
observe during the day at the Chilean site, but very demanding
observations which require good pointing such as high fidelity
mosaicing at 230 GHz and 345 GHz, or which require both good pointing
and good phase stability, such as 690 GHz and 850 GHz single pointing
observations, will mostly take place at night. This situation will be
completely analogous to the VLA: while the VLA observes 24 hours a
day, the most demanding VLA observations are performed at night as
well.
|
| Mauna Kea | Chile |
| wind speed | 1.2 | 2.5 |
|
rms phase | 6 | 3 |
|
opacity | 3 | 1.2 |
Table 1: Wind speed, rms phase fluctuations, and opacity
are generally higher during the day than during the night,
approximately by the factor listed in the above table.
While the median winds on the Chilean site are higher than on the
Mauna Kea site, the peak winds are not so different on the two sites.
The highest measured wind velocity on the Chilean site between 95 May
and 96 April is 33 m/s (73 mph), while the highest measured wind
velocity on the Mauna Kea/VLBA site was 28.8 m/s (64 mph). The 5000 m
Chilean site typically has an atmospheric pressure of 550 mbar, while
the 3750 m Mauna Kea site has an atmospheric pressure of 650 mbar.
The destructive force of the wind is proportional to the air pressure
times the wind velocity squared, so the highest wind on the Chilean
site was about 20% more destructive than the highest wind in the
Mauna Kea site. However, it should be noted that a statistic as
volatile as maximum wind velocity should be sampled over several
years. Hurricanes with much higher wind velocities occasionally
strike Mauna Kea.
Jingquan Cheng (1996, in preparation) has calculated the static
pointing error which the conventional and slant-axis MMA antennas
would incur from a constant 9 m/s wind. The calculation results
depend upon the orientation of the wind velocity vector with respect
to the antenna azimuth and the antenna elevation, but we simplify the
situation by averaging over azimuth and elevation, resulting in taking
3.5 arcseconds to be representative of these static pointing errors
for the conventional antenna in a 9 m/s wind (see Appendix A for a
justification of this number). The slant-axis design has pointing
errors of about 1.3 arcseconds in a 9 m/s wind, though there are other
contributions to the slant-axis pointing errors which have yet been
quantified, such as slop in the big bearing and misalignment of the
encoders. From this result, we assume that the slant-axis antenna
will likely meet the MMA pointing specification. However, the
slant-axis design is currently not in favor because of its poor close
packing properties, whereas the conventional design will probably be
able to have suitably small minimum antenna separations (Holdaway,
1996). Hence, we focus our analysis on the conventional design.
The deforming power of the wind is proportional to 
, and even
with zero wind velocity, the MMA antennas will have some residual
pointing error 
, the native pointing of the antennas in
near perfect conditions. Assuming that the wind induced and zero
velocity pointing errors add quadratically and neglecting thermal
effects, the pointing error p as a function of velocity will be
something like
Jingquan Cheng estimates is about 0.7 arcseconds. For the
median Chilean wind speed of 6 m/s, the pointing errors are
1.7 arcsecond, and for the median night time Chilean wind speed of
3.5 m/s, the pointing errors are 0.9 arcseconds. It appears that
during most night time conditions on Chajnantor, the pointing errors
will be limited by the native pointing and not by
the wind. Submillimeter observations can be greatly helped if we can
find a way to inexpensively reduce .
While this is all quite encouraging, it may be possible to do even
better since some of the static wind induced pointing errors will vary
slowly and can be removed by frequent pointing calibration. The
short time scale power spectrum of wind speed fluctuations is usually
fairly steep. For frequencies above 0.01 Hz, the wind speed
fluctuations are often modeled by the Davenport (1962) spectrum,
which is a power law decreasing as frequency raised to the -1.67
power. Recent measurements of the wind spectrum at Green Bank
obtained a spectrum with a power law very close to the Davenport
spectrum. In late May 1996, we modified our site testing system in
Chile to record the wind speed and direction every 3.5 s for a full
hour every 3.5 hours. Figure 5 shows an example of
the wind speed and direction over a one hour period. While some one
hour profiles do show significant change in wind speed or direction,
many show very constant wind direction and fairly constant wind speed.
Our investigations indicate that the wind spectrum at Chajnantor
is usually significantly flatter than the Davenport spectrum.
Figure 6 shows the wind speed spectrum for one day
with a fit power law exponent of -1.04. Typically, the power spectrum
turns over below 0.005 - 0.01 Hz.
One result of the fast switching requirement on the antenna design is
that the lowest resonant frequency must be pushed as high as possible.
Modeling of the current design reveals a lowest resonant frequency of
6.7 Hz. Even with the flatter power spectrum, the wind has very
little power at this high frequency. We assume that the antennas do
not react to the wind resonantly, but rather the effects of the time
dependent wind on the antenna can be approximated by a series of
different static wind induced pointing errors. Under this
approximation, we can use the wind time series to calculate the time
series of wind induced pointing errors, and hence, the rms pointing
errors which the MMA antennas would experience. (Jingquan Cheng is
pursuing a proper dynamic analysis of the MMA antenna designs which
should complement this memo. Inclusion of the dynamic wind
calculation in the pointing error analysis is expected to increase the
pointing error.) Since a large component of the wind velocity is
constant on 10-30 minute time scales, it should be possible to
calibrate the pointing on a nearby calibrator source every
10-30 minutes to remove the effects of the constant component of the
wind velocity.
For the analysis and presentation of the residual pointing errors
after pointing calibration has been performed, we do not consider the
native pointing error which we introduced above. It
should remembered that such a term should be added in quadrature, so
that a wind induced pointing error of about 0.7 arcseconds will be
required to get a total pointing error of 1 arcsecond. We assume that
the pointing calibration can be achieved in just a few seconds, which
is quite reasonable as we shall see below. So, the rms static
pointing error will be
while the residual pointing error after calibration will be
where the time t runs through the time interval between pointing
calibrations, and 
is the wind velocity at the start of
that time interval.
Optimally, we would like to be able to remove some of the power in the
wind fluctuations from the antenna pointing. However, to do this
requires pointing calibration more often than every 100 s since the
power spectrum turnover is typically around 0.01 Hz. Instead, we will
assume pointing calibration intervals which sound reasonable, such as
10, 20, and 30 minutes. However, since these calibration intervals
are all beyond the spectral turnover, there is not a great deal of
power in the long term fluctuations which they correct for, and they
are more or less equally effective. However, there is usually a great
deal of power in a constant wind velocity term, and even pointing
calibration every 30 minutes will be effective at removing this
constant component.
Figure 7 shows the cumulative distributions of rms day
time pointing errors on Chajnantor for 1996 May 19 through July 10, as
calculated from both the static wind pointing model in
Equation 2 and from the pointing calibration model in
Equation 3. The calibration interval was 10 minutes.
Figure 8 shows the distributions of the rms night
time static and calibrated pointing errors for the same time period.
The period which we monitored has some of the windiest conditions of
the year, yet post calibration median wind induced pointing is only
about 1.5 arcseconds during the day and 0.5 arcseconds during the
night. This is very encouraging, and indicates that the conventional
antenna may meet the specification of 1 arcsecond pointing overall for
the best 50% of the time. Again, note that the stiffer slant-axis
antenna will have much better pointing than the conventional design.
While we are not suggesting changing the design specification,
sub-arcsecond pointing would greatly benefit submillimeter
observations, even permitting mosaics at submillimeter wavelengths, so
surpassing the pointing specification would positively impact the science
which could be done with the MMA.
Before we assume that calibrating the mean effects of the wind on
pointing can get the conventional design antenna close to the pointing
specification, we need to determine if it is reasonable to perform
pointing calibration every 10-30 minutes.
Frequent pointing calibration will not be a major fraction of
observing time. In fact, the antenna designers are already planning
to perform pointing calibration every 30 minutes or so to correct for
thermally induced pointing errors (Napier, 1995). We can perform
pointing calibration on the same quasars we plan to use for fast
switching phase calibration. The optimal frequency to use for
pointing will depend upon the details of the dependence of system
noise with frequency and the dependence of the flat spectrum quasar's
flux density with frequency. Holdaway, Owen, and Rupen (1994) found
that the flux of their sample of flat spectrum quasars decreased as
between 8 and 90 Ghz. Since the beam size is inversely
proportional to frequency, if system noise increases more steeply
than 
(which is likely if the receiver and atmospheric
noise dominates), pointing determinations are more sensitive at low
frequencies, and if system noise increases less steeply than
(which is likely if ohmic losses and ground pickup
dominate), pointing is more sensitive at higher frequencies, at least
up to frequencies where the quasar fluxes begin to fall off more
rapidly. For the time being, we will assume that pointing will be
calibrated to 90 GHz. The 8 m MMA antennas will have a HPBW of about
100 arcseconds at 90 GHz, so 1 arcsecond pointing will be 1/100 of the
beam, which will be technically challenging. We must also know how to
transfer the 90 GHz pointing to higher frequency bands. At the VLA,
constant collimation offsets between the different observing bands are
assumed. However, since the MMA's situation is more demanding, we might
be forced to investigate elevation (or other) dependencies of the
collimation offsets between the various observing bands to accurately
transfer the 90 GHz pointing to higher frequency bands.
Assuming the technical challenges of transferring the pointing
solution from the pointing band to the higher bands can be solved, we
next address how bright a source we need to solve for the pointing to
an accuracy of 1/100 of a beam. A simple analysis of the classical
five point pointing procedure performed interferometrically indicates
that the pointing error 
as a fraction of a beam
is roughly
where 
is the noise per visibility per point of the five
point, N is the number of antennas, and S is the source strength
at the beam center. Since the constant component of the wind will
have different effects on the antennas as they point in different
directions, we must point on quasars which are very close to the
target source. At this point, we don't know exactly how close, but
lets assume that 5 degrees distant on the sky is close enough. Foster
(1994) showed that Holdaway, Owen, and Rupen's (1994) 90 GHz source
counts predict that a quasar of 0.5 Jy or brighter is, on average,
about 5 degrees away from any target source. At 90 GHz, the noise per
visibility at full continuum bandwidth of 16 GHz (we will average both
polarizations) and 
of 30 K, leading to a noise per
visibility of 0.016 Jy in one second. So, integrating only 1 s for
each of the five points results in a formal error in the fractional
beam width of 0.007. The full five point, plus travel time, would
take on the order of 20 s. If such pointing were performed every 10 minutes,
the noise would be increased by about 2%.
When the wind velocity speed or direction display large fluctuations,
there will be an additional noise-like error in the pointing solution
due to the wind noise. However, when the wind is fluctuating enough
for this to be a large problem, frequent pointing calibration will not
work well anyway.
We still need to look critically at the pointing error calculations of
Cheng when they are available, but it is clear that the MMA antennas
do not need to meet the 1 arcsecond pointing specification for the
deflections caused by a 9 m/s wind. It is likely that 1 arcsecond
pointing can be achieved much of the time during the night when the
wind velocities are much lower. Also, the wind velocities are often
constant enough so that 1 arcsecond pointing could be achieved in higher
velocity winds if pointing calibration were performed on time scales
of 10 minutes on a quasar within 5 degrees of the target source. Such
pointing calibration is feasible from a signal to noise point of
view, and does not significantly add to the noise on the target
source, but the precise tranfer of the pointing solution from 90 GHz
to the higher frequencies may present technical challenges.
Since wind induced night time pointing errors scaled from Cheng's
simulations will often be under half an arcsecond, the pointing will
often be limited by the zero velocity pointing. Improving the pointing
accuracy to better than 1 arcsecond will improve the 690 GHz and
850 GHz performance, even permitting moderate dynamic range mosaics.
It is therefore important to design the MMA antennas with as low a
zero wind velocity pointing error as we can reasonably afford.
Jingquan Cheng (1996, in preparation) has performed static
calculations of the bending of the conventional design antenna
components due to wind loading in a 9 m/s wind using the Autocad
package. However, the MMA antenna pointing errors induced by the wind
will depend strongly on the elevation angle (EL) and the azimuth angle
(AZ) with respect to the wind. Given the pointing error as a function
of wind AZ and EL, the distribution of directions from which the wind
blows, and the distribution of observed AZ and EL, we can estimate the
typical pointing error which the conventional design antenna will
suffer in a 9 m/s constant wind. The distribution of observed AZ and
EL depends upon the distribution of sources on the sky and upon the
observational strategy. While it is difficult to guess the use of a
telescope a decade before it is built, two different source
declination distributions and observing strategies, one for generic
interferometry and one for mosaicing, give very similar average
pointing errors.
We considered five different sorts of source distributions for the MMA:
- uniformly distributed sources, such as extragalactic sources
(with the exception of the Magellanic Clouds) and nearby stars.
- Galactic sources (with the exception of the Galactic Center)
located within about 5 degrees from the Galactic plane.
We assumed that the distribution of Galactic observations
will be peaked towards the center and fade out at the anti-center.
We took the ad hoc distribution of
, where
is the Galactic longitude.
- Sources within the solar system will be mainly between
declinations -25 and +25, determined by the tilt of the
earth's axis and the inclination of the planets' orbits with
respect to the earth's orbit.
- Galactic center observations.
- Observations of the LMC and SMC.
For generic interferometry, we assumed the breakdown of observed
objects would follow: 40% extragalactic, 45% galactic, 5% solar
system, 5% Galactic center, and 5% LMC/SMC. This density of sources
as a function of declination is shown in Figure 9. For
mosaic objects, which favor large sources, we assume: 23%
extragalactic, 55% galactic, 5% solar system, 5% Galactic center,
and 12% LMC/SMC. This density of sources as a function of
declination is shown in Figure 10. Modest changes in the
mixes of the various source distributions have a very small effect
on the resulting AZ-EL distribution.
For generic interferometry, we assume that we will be able to observe
out to hour angles such that the air mass is 1.5 times greater than
the transit air mass. For mosaicing observations, we assume that we
will be able to observe only to hour angles of +/-2 before shadowing
becomes a problem. The observing strategy does not have a strong
effect on the resulting AZ-EL distribution.
We have simulated observations at declinations -88, -86, ... +58 (the
effective range of the Chajnantor site), and the hour angle ranges
which result from the above assumptions, with hour angle increments of
0.05, throwing out any observations below an elevation limit of
8 degrees. We have then binned each observed point in AZ and EL,
weighting by the density of sources at that declination and inversely
with the length of the tracks in hour angle. The resulting
distribution of observed AZ and EL for the generic interferometry case
is shown in Table 2, and the mosaicing case is
shown in Table 3. We have also integrated through
azimuth to obtain the distributions of observing elevation angle for
these two cases (see Figure 11). Such curves will probably
be useful for other unrelated calculations in the future.
Cheng's pointing errors included terms for both the yoke and the dish,
but it was not possible to calculate these terms for all possible
combinations of AZ and EL. Cheng calculated yoke pointing errors at
15 degree intervals in elevation and 30 degree intervals in azimuth,
and dish pointing errors at 30 degree intervals in both elevation and
azimuth. A few calculation results showed anomalously high values of
the pointing error, and they were smoothed to avoid calculation error.
Component pointing errors which could not be calculated were estimated
by hand. The yoke and dish pointing errors were scalar added
(admittedly a worst case). We further relied upon symmetry conditions
to fill in the table. Linear 2pt interpolation was used to get
pointing errors on a grid which was compatible with the distribution
of observed AZ-EL. An example grid of the pointing errors is shown in
Table 4. It should be stressed that the results of
these calculations are somewhat uncertain, as they result from
multiple vector components (even multiple components within the yoke
and dish components) which may add or cancel. In addition, these
pointing errors do not include the results of dynamic wind calculations,
which would tend to increase the pointing errors.
Finally, we looked at the distribution of wind directions when the
wind speed was greater than 6 m/s, shifting the pointing error
function appropriately and integrating the pointing error over AZ EL
weighting by the observing distribution, then integrating over the
wind direction distribution. The wind direction distribution is
peaked at about AZ=280 deg with a spread of about 45 deg. This
procedure assumes that the distribution of observing AZ EL and the
wind direction distribution are independent. The generic
interferometry case resulted in a pointing error of about
3.4 arcseconds, and the mosaicing case resulted in a pointing error of
about 3.5 arcseconds. The mosaic case has a larger pointing error
because the small hour angle range results in more observing at higher
elevations, and the conventional design antenna pointing errors are
larger at high elevations.
Cheng, Jingquan, 1993,
``Slant-Axis Antenna Design II'',
MMA Memo 101.
Cheng, Jingquan, 1996, MMA Memo on antenna pointing, in preparation.
Cornwell, T.J., Holdaway, M.A., and Uson, Juan, 1994,
``Radio-interferometric Imaging of Very Large Objects: Array Design'',
A&A 271, 693-713.
Davenport, A.G., 1962, ``Buffeting of a Suspension Bridge by Storm Winds'',
ASCE Journal of Structural Division, 88 (ST2) 233-68.
Foster, S.M., 1994, ``Angular Distance to MMA Calibrators Based on
90 GHz Source Counts'', MMA Memo 124.
Holdaway, M.A., Owen, F.N. and Rupen, M.P., 1994, ``Source Counts at 90 GHz'',
MMA Memo 123.
Holdaway, M.A., 1996, ``Evaluating the Minimum Baseline Constraints for
the MMA D Array'', MMA Memo 155.
Napier, P.J., et al., 1995, ``Antennas for the
Millimeter Wave Array: The MDC Antennas Working Group'', MMA Memo 145.
|
| EL |
| 5. | 15. | 25. | 35. | 45. | 55. | 65. | 75. | 85. |
|
AZ | | | | | | | | | |
| 10. | 0.720 | 2.082 | 1.524 | 1.256 | 1.221 | 0.912 | 0.629 | 0.424 | 0.153 |
|
30. | 0.000 | 0.564 | 1.326 | 1.321 | 1.162 | 0.905 | 0.652 | 0.391 | 0.154 |
|
50. | 0.000 | 0.000 | 0.228 | 1.221 | 1.113 | 0.893 | 0.630 | 0.415 | 0.131 |
|
70. | 0.000 | 0.000 | 0.000 | 0.355 | 1.054 | 0.907 | 0.647 | 0.424 | 0.160 |
|
90. | 0.000 | 0.000 | 0.000 | 0.000 | 1.080 | 0.979 | 0.775 | 0.465 | 0.153 |
|
110. | 0.000 | 0.000 | 0.000 | 0.000 | 1.493 | 1.422 | 1.203 | 0.937 | 0.146 |
|
130. | 0.000 | 0.000 | 0.000 | 0.353 | 1.301 | 1.027 | 0.685 | 0.445 | 0.410 |
|
150. | 0.000 | 0.000 | 0.145 | 1.913 | 2.057 | 1.281 | 0.780 | 0.428 | 0.229 |
|
170. | 0.000 | 0.010 | 0.463 | 1.324 | 1.770 | 1.759 | 0.853 | 0.435 | 0.250 |
|
190. | 0.000 | 0.010 | 0.461 | 1.337 | 1.758 | 1.760 | 0.833 | 0.446 | 0.249 |
|
210. | 0.000 | 0.000 | 0.132 | 1.890 | 2.056 | 1.290 | 0.770 | 0.408 | 0.287 |
|
230. | 0.000 | 0.000 | 0.000 | 0.333 | 1.281 | 1.027 | 0.685 | 0.455 | 0.353 |
|
250. | 0.000 | 0.000 | 0.000 | 0.000 | 1.471 | 1.423 | 1.183 | 0.947 | 0.158 |
|
270. | 0.000 | 0.000 | 0.000 | 0.000 | 1.021 | 0.978 | 0.775 | 0.477 | 0.140 |
|
290. | 0.000 | 0.000 | 0.000 | 0.309 | 1.111 | 0.872 | 0.682 | 0.412 | 0.160 |
|
310. | 0.000 | 0.000 | 0.205 | 1.198 | 1.078 | 0.870 | 0.642 | 0.415 | 0.155 |
|
330. | 0.000 | 0.544 | 1.306 | 1.328 | 1.186 | 0.882 | 0.675 | 0.402 | 0.142 |
|
350. | 0.721 | 2.084 | 1.495 | 1.236 | 1.231 | 0.889 | 0.641 | 0.401 | 0.140 |
Table 2: Distribution of observed AZ-EL, in percent time, for the
generic interferometry case in which sources may be observed until
the elevation results in an airmass which is 1.5 times higher than
the transit airmass.
|
| EL |
| 5. | 15. | 25. | 35. | 45. | 55. | 65. | 75. | 85. |
|
AZ | | | | | | | | | |
| 10. | 0.641 | 1.940 | 1.611 | 1.422 | 1.594 | 1.230 | 0.909 | 0.647 | 0.273 |
|
30. | 0.000 | 0.115 | 0.549 | 1.139 | 1.494 | 1.185 | 0.923 | 0.573 | 0.238 |
|
50. | 0.000 | 0.000 | 0.000 | 0.000 | 0.316 | 1.038 | 0.919 | 0.586 | 0.243 |
|
70. | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.265 | 0.985 | 0.692 | 0.236 |
|
90. | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.995 | 0.768 | 0.248 |
|
110. | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.616 | 1.532 | 0.238 |
|
130. | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 1.245 | 0.824 | 0.607 |
|
150. | 0.000 | 0.000 | 0.000 | 0.000 | 0.346 | 2.053 | 1.457 | 0.757 | 0.493 |
|
170. | 0.000 | 0.000 | 0.045 | 2.007 | 5.994 | 4.030 | 1.658 | 0.753 | 0.312 |
|
190. | 0.000 | 0.000 | 0.046 | 2.042 | 6.139 | 4.175 | 1.760 | 0.842 | 0.464 |
|
210. | 0.000 | 0.000 | 0.000 | 0.000 | 0.346 | 2.053 | 1.457 | 0.757 | 0.493 |
|
230. | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 1.245 | 0.824 | 0.607 |
|
250. | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.616 | 1.532 | 0.238 |
|
270. | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.995 | 0.768 | 0.248 |
|
290. | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.265 | 0.985 | 0.692 | 0.236 |
|
310. | 0.000 | 0.000 | 0.000 | 0.000 | 0.316 | 1.038 | 0.919 | 0.586 | 0.243 |
|
330. | 0.000 | 0.115 | 0.549 | 1.139 | 1.494 | 1.185 | 0.923 | 0.573 | 0.238 |
|
350. | 0.661 | 1.903 | 1.562 | 1.368 | 1.520 | 1.155 | 0.830 | 0.564 | 0.179 |
Table 3: Distribution of observed AZ-EL, in percent time, for the
mosaicing case in which more galactic and LMC/SMC sources are observed,
and sources are only observed for +/- 2 hours from transit.
|
| EL |
| 7 | 22 | 37 | 52 | 67 | 82 |
|
AZ | | | | | | |
| 0 | 2.27 | 2.43 | 2.82 | 2.85 | 3.28 | 4.28 |
|
30 | 3.08 | 2.88 | 2.86 | 3.28 | 3.85 | 4.22 |
|
60 | 3.97 | 3.54 | 3.88 | 4.13 | 3.65 | 2.99 |
|
90 | 3.10 | 3.25 | 3.00 | 3.10 | 3.08 | 3.11 |
|
120 | 3.22 | 3.42 | 3.38 | 3.48 | 3.62 | 3.27 |
|
150 | 2.64 | 2.86 | 2.82 | 3.19 | 3.87 | 4.38 |
|
180 | 2.14 | 2.65 | 2.83 | 3.19 | 3.84 | 4.38 |
|
210 | 2.64 | 2.86 | 2.82 | 3.19 | 3.87 | 4.38 |
|
240 | 3.22 | 3.42 | 3.38 | 3.48 | 3.62 | 3.27 |
|
270 | 3.10 | 3.25 | 3.00 | 3.10 | 3.08 | 3.11 |
|
300 | 3.97 | 3.54 | 3.88 | 4.13 | 3.65 | 2.99 |
|
330 | 3.08 | 2.88 | 2.86 | 3.28 | 3.85 | 4.22 |
Table 4: Pointing error, in arcseconds, for the conventional
design antenna, as a function of azimuth angle with respect
to the wind direction and elevation angle.
Figure 1: First, second, and third quartile wind speeds on Mauna Kea as
a function of month of year.
Figure 2: First, second, and third quartile wind speeds in Chile as
a function of month of year.
Figure3: First, second, and third quartile wind speeds on Mauna Kea as
a function of local hour of day.
Figure 4: First, second, and third quartile wind speeds in Chile as
a function of local hour of day.
Figure 5: Example of the wind speed and direction on Chajnantor for May 21, 1996,
3:34-4:34 UT (around midnight local time).
Figure 6: Power spectrum of wind speed on Chajnantor for June 17, 1996.
The fit power law slope is -1.04, much flatter than the Davenport
spectrum of -1.67.
Figure 7: Cumulative distributions of Chajnantor day time rms pointing errors
before and after calibration for part of the 1996 winter season.
Figure 8: Cumulative distributions of Chajnantor night time rms pointing errors
before and after calibration for part of the 1996 winter season.
Figure 9: Assumed distribution of sources for generic interferometry.
Figure 10: Assumed distribution of sources for mosaic observations.
Figure 11: Distribution of observing elevation for the generic interferometry,
1.5 airmass case and the mosaicing, 2 hour case.