\documentstyle[12pt,psfig]{article} 

\begin{document}

\title{\bf ALMA Memo 384\\
Atmospheric Transparency at Chajnantor and Pampa la Bola}
\author{Simon J. E. Radford and Bryan J. Butler\\
National Radio Astronomy Observatory\\
\\
Seiichi Sakamoto\\
National Astronomical Observatory of Japan\\
\\
Kotaro Kohno\\
Nobeyama Radio Observatory}
\date{2001 August 2}
\maketitle

\begin{abstract} 

Measurements with 220 and 225\,GHz tipping radiometers 
demonstrate the atmosphere over both Chajnantor
and Pampa la Bola has exceptional transparency,
better than observed over Mauna Kea.
These measurements indicate, however,
the atmosphere is more transparent 
at Chajnantor than at Pampa la Bola. 
For hourly median optical depths from 
1999 June through 2000 December,
the median at Pampa la Bola
is 0.011 larger than at Chajnator and
the median normalized difference is
$[\tau_{220} ({\rm Bola}) - \tau_{225} ({\rm Chaj.})]/\tau_{225}
= +0.23$.
Side-by-side measurements at Chajnantor
in 2001 April--May confirm 
the data from the two instruments can be directly compared.
The measured transparency differences imply Chajnantor enjoys
a significant advantage in observing time or sensitivity, 
especially for observations at submillimeter wavelengths.

\end{abstract}

\subsection*{Introduction}

Atmospheric transparency presents a fundamental limitation to 
the speed and sensitivity of observations at millimeter
and submillimeter wavelengths. 
In planning the ALMA project, therefore, the 
partner institutions have expended considerable effort to 
assess and select an outstanding site in the high Andes of
northern Chile. 
This area, around Cerros Chajnantor and Chasc\'on, 
has been designated a science preserve by the Chilean goverment. 
It has exceptional 
atmospheric transparency, ranking among the premier
sites for millimeter and submillimeter 
wavelength astronomy.
In particular, the area enjoys better conditions than 
Mauna Kea
(Figure \ref{fig:cdf}; Radford \& Chamberlin 2000).

Within the science preserve, measurements of atmospheric 
transparency have been carried out at two particular locations.
Since 1995 April, the NRAO has operated a 225\,GHz tipping 
radiometer on the Llano de Chajnantor (5050\,m)
about 4.3\,km south-southwest of Cerro Chajnantor
(Radford \& Holdaway 1998).
In 1996 July, the NRO installed a similar 
220\,GHz tipping radiometer at Pampa la Bola,
about 250\,m lower than and 8\,km NE of the NRAO instrument
(Ishiguro et al.\ 1998).
Data from these instruments
confirm both sites are excellent but
suggest the transparency at Chajnantor is
significantly better than at Pampa la Bola.

\subsection*{Instruments}

The NRAO tipping radiometer (Liu 1987; McKinnon 1987)
is a DSB heterodyne receiver
operating at 225\,GHz with a 1.0--1.5\,GHz IF bandpass.
(Because the earlier memos give inconsistent descriptions of
the passband, we have reconfirmed the actual band width.)
An internal chopper continuously switches the receiver input
between two calibration loads ($45^\circ$C and $65^\circ$C)
and an offset parabolic mirror that scans the sky. 
The radiometer measures the atmospheric transparency every 
10\,min except for one hour every 4.5\,h, when the transparency 
measurements are suspended while the receiver measures fluctuations
in the sky brightness.
Since 1998 June, the instrument clock has been synchronized 
to within one second of UTC by a GPS receiver. 
Before that, the clock was kept within a few minutes of 
UTC by monthly telephone calls to the NIST time service.
Through 2001 July, the instrument has operated
84\% of the time. Because of various 
instrument failures, however,
data are sparser in early 2000 than in other years. 

The NRO tipping radiometer is also a DSB heterodyne receiver
(Kohno et al.\ 1995).
Although known as the 220\,GHz radiometer, it
actually operates at 218.5\,GHz with a 1.0--1.4\,GHz IF bandpass.
It determines the transparency about once per minute.
The system clock is set during periodic maintenance visits.

Both instruments measure the sky brightness 
at several zenith angles to determine the atmospheric transparency.
For a conventional simple atmospheric model of a plane
parallel isothermal slab, the (monochromatic) sky
brightness temperature, 
\begin{equation}
T_{\rm sky}(z) = T_{\rm atm} (1-e^{-\tau A}),  
\end{equation}
where $\tau$ is the atmospheric optical depth at the zenith,
$T_{\rm atm}$ is the effective atmospheric radiation temperature,
and $A=\sec(z)$ is the airmass at zenith angle $z$. 
Both radiometers make single sided tips from
the zenith down towards the horizon. 
As a result, they might measure systematically higher or
lower optical depths if they were not precisely level.
At Chajnantor, the NRAO tipper scans toward the 
eastern horizon.
At Pampa la Bola, the NRO instrument scans toward the
western horizon.

\subsection*{Data}

Simultaneous data from both instruments exist for most of the time 
since 1999 June and sporadic data exist for 1996 and 1997
(Table 1).
All months of the year are represented except January and
February, which are absent because of complementary instrument 
failures in 2000 and 2001. During 2001 March--May, the NRAO 
radiometer suffered a partial software malfunction. Those data 
have been edited accordingly, but remain lower quality than
for other periods.

For detailed comparison, the data were 
paired by selecting the first Pampa la Bola measurement  
within 1 min of each Chajnantor measurement. 
This synchronization is perhaps overly strict.
The sites are 8\,km apart, which 
corresponds to a 20\,min delay at
the median surface wind speed, 6.5\,m\,s$^{-1}$
(Radford \& Holdaway 1998), and 
winds aloft tend to be faster than
surface winds.
Furthermore, although the relative synchronization
of the instrument clocks appears adequate, the
actual synchronization precision is unknown. 
Because substantial changes in transparency
do not occur quickly, 
exact data synchronization is not essential 
for meaningful site comparison
and sampling the same diurnal, seasonal, and weather cycles
is sufficient.
For an overall view, therefore, the median optical depths
were determined for each hour from 
1999 June through 2001 December
when data were available for both sites. 

Both instruments see similar overall weather patterns  
(examples in Figures \ref{fig:time_199907}, 
\ref{fig:time_199910}, \& \ref{fig:time_200010}). 
Substantial changes in transparency do not 
happen quickly, but occur over periods of hours or
longer.

For 1999 June and subsequent months,
the paired data are generally well correlated,
with  linear correlation coefficients $r \ge 85$\%
(examples in Figures \ref{fig:stats_199907}, 
\ref{fig:stats_199910}, \& \ref{fig:stats_200010}). 
As a rule, however, the measured transparency
is better at Chajnantor than at Pampa la Bola.
The monthly median optical depths at
Pampa la Bola
are typically between 0.01 and 0.02 larger
than at Chajnantor (Table 1).
In relative terms, 
the monthly median normalized differences,
$[\tau_{220} ({\rm Bola}) - \tau_{225} ({\rm Chaj.})]/\tau_{225}$
are typically $+0.1$ to $+0.4$.

A similar difference between the sites is evident from
comparison of the hourly median optical depths 
(Figure \ref{fig:stats_boxcar}).
In these data, the median at Pampa la Bola,
$ \tau_{220}  ({\rm Bola})= 0.054$,
is  0.011 larger than the median at
Chajnantor, $\tau_{225} ({\rm Chaj.}) = +0.043$
(Table 1). 
The median normalized difference is
$[\tau_{220} ({\rm Bola}) - \tau_{225} ({\rm Chaj.})]/\tau_{225}
= +0.23$.

The paired data from 1996 and 1997, on the other
hand, are often poorly correlated,
suggesting an instrument problem such as a
clock offset. 
Although these data also indicate better conditions
at Chajnantor, they are not a reliable basis 
for comparison and are excluded from the overall
statistics.

\subsection*{Instrument Comparison}

The two instruments operate with different frequencies (218.5
and 225\,GHz) and bandwidths (1.0--1.4 and 1.0--1.5\,GHz). 
Might these differences explain the observed results? 

For these radiometer parameters and 1\,mm of 
water vapor over a 5000\,m high site, the ATM 
atmospheric model (Pardo et al.\ 2001) predicts 
$ \tau_{220} = 0.047$ and $ \tau_{225} = 0.053$,
or 
$(\tau_{220} - \tau_{225})/\tau_{225} = -0.11$.
The difference is largely caused by an O$_3$ line in the 
upper side band of the 225\,GHz radiometer.
This prediction of {\it larger\/} 
optical depths at 225\,GHz with the NRAO radiometer 
cannot explain, however, the observations
of larger optical depths at 220\,GHz with the NRO
radiometer on Pampa la Bola.

Intercomparison observations have been made on two occasions. 
On 1994 November 5--6, the two radiometers 
were run side by side at the Paranal base camp ($\approx 2000$\,m) for 
somewhat more than 24\,h. This test indicated good agreement, 
$|\tau_{220} - \tau_{225}| < 0.01$ (Holdaway et al.\ 1996) when the 
median $\tau_{220}$ was 0.13.
Conditions at both Chajnantor and Pampa la Bola
are considerably better than at the Paranal base camp,
however, and the observed differences between the high sites are
about the same magnitude as the precision of the agreement
in the Paranal comparison.

From 2001 April 24 to May 2, therefore,
the two instruments were operated
side-by-side at Chajnantor,
scanning parallel to each other. 
The weather was variable, including very good 
($\tau_{225} < 0.03$) and
mediocre ($\tau_{225} \approx 0.3$) conditions
(Figure \ref{fig:time_200104}).
Over this range, 
the measured optical depths agree very well
(Figure \ref{fig:stats_200104}).
The median normalized difference, 
$(\tau_{220} - \tau_{225})/\tau_{225} = -0.03$,
has the same sense as the model prediction,
albeit with a smaller magnitude.
During this comparison, the NRAO radiometer measured slightly 
larger optical depths than the NRO instrument.

The agreement between the instruments 
during these intercomparisons
was very good, 
much better than the typical observed
difference between the sites. 
Hence the data for Pampa la Bola and Chajnantor 
can be directly compared.

\subsection*{Implications}

At 220/225\,GHz, the absolute value of the measured difference 
in atmospheric transparency between Chajnantor 
and Pampa la Bola is small. 
The differences in the monthly median optical depths 
$ \tau_{220}  ({\rm Bola}) - \tau_{225} ({\rm Chaj.})$ 
generally lie between $+0.01$ and $+0.02$ (Table 1).
This small transparency difference implies, however, 
a substantial difference in observing time, especially 
at submillimeter wavelengths.

The integration time, $t$, required to acheive a certain sensitivity
depends on the square of the system noise, $T_{\rm sys}$,
\begin{equation}
 t \propto T_{\rm sys}^2 = e^{2\tau A} \left[ T_{\rm rec} + 
  T_{\rm atm} \left( 1 - e^{-\tau A} \right) \right]^2 ,
\end{equation}
\noindent
where $T_{\rm rec}$ is the receiver temperature.%, 
%$T_{\rm atm}$ is the effective atmosphere temperature, and
%$A = \sec(z)$ is the airmass at zenith angle $z$. 
(Secondary effects, including ground spillover and the
cosmic background radiation, have been neglected.) Then 
to reach the same sensitivity in
observations under two conditions, $\tau_1$ and 
$\tau_2$,
the ratio of the required integration times
\begin{eqnarray}
 t_1/t_2 & = & (T_{\rm sys,1}/T_{\rm sys,2})^2 \\
         & = & e^{2(\tau_1 - \tau_2)A} 
         \left[ \frac{  T_{\rm rec} +   T_{\rm atm} \left( 1 - e^{-\tau_1 A} \right)}
                     {  T_{\rm rec} +   T_{\rm atm} \left( 1 - e^{-\tau_2 A} \right)} \right]^2.
\end{eqnarray}

Based on observations at Pampa la Bola (and Chajnantor)
with a Fourier transform spectrometer,
Matsushita et al.\ (1999, 2000) derive linear regressions
between the optical depths at different frequencies,
$\tau(\nu) = a(\nu)\, \tau_{220} + b(\nu)$ (Table 2). 
These measured regressions allow an extrapolation to 
higher frequencies of the measured 
difference between the transparency at Pampa la Bola and
Chajnantor.
(This extrapolation may not be valid for other sites.)
The ALMA project goals are receivers with noise temperatures
limited to a few times the quantum limit, 
for example $T_{\rm rec} \le 5 h \nu / k$
(Wild \& Payne 2001).
At tropical latitudes, the median airmass for transit 
observations of uniformly distributed 
sources at $z<60^\circ$ is $A = 1.1$.
Take, as an illustration, these factors together with
$ \tau_2 =  0.04$, which is the first quartile of the 
long term distribution at Chajnantor (Figure \ref{fig:cdf}),
and
$(\tau_1 - \tau_2)/\tau_2 = +0.25$, which is typical 
for the measured difference between Pampa la Bola and
Chajnantor.
Then the observing time (or sensitivity) advantage enjoyed by Chajnantor, 
which is modest, but significant, at millimeter wavelengths, 
becomes dramatic 
for submillimeter observations (Table 2). 
Considering median conditions or observations at a larger 
airmass would further enhance the contrast between the sites.
 

\subsection*{Conclusions}

At 220/225\,GHz, both Chajnantor and 
Pampa la Bola have better atmospheric 
transparency than found at Mauna Kea.
The measured transparency is, however, better 
at Chajnantor than at Pampa la Bola. 
For hourly median optical depths from 
1999 June through 2000 December,
the median at Pampa la Bola
is 0.011 larger than at Chajnator and
the median normalized difference is
$[\tau_{220} ({\rm Bola}) - \tau_{225} ({\rm Chaj.})]/\tau_{225}
= +0.23$.
Side-by-side measurements with both instruments at Chajnantor
in 2001 April--May confirm the data 
from the two instruments can be directly compared.
The measured transparency difference implies
Chajnantor enjoys
a significant advantage in observing time or sensitivity,
especially for observations at submillimeter wavelengths.

%\clearpage


\subsection*{Acknowledgements}

We thank Angel Ot\'arola for 
keeping the instruments functioning and
Mark Holdaway, Frazer Owen, and Bob Brown
for helpful comments and suggestions.

\subsection*{References}

\def\reference{\hangindent=\parindent \hangafter=1 \noindent}
\parskip=1pt

\reference Holdaway, M. A., Ishiguro, M., Foster, S. M., Kawabe, R., 
Kohno, K., Owen, F. N., Radford, S. J. E., \& Saito, M., 1996, MMA Memo 152

\reference Ishiguro, M., et al., 1998, Proc.\ SPIE 3357, 244

\reference Kohno, K., Kawabe, R., Ishiguro, M., Kato, T., Ot\'arola, A., 
Booth, R., \& Bronfman, L. 1994, 
NRO Tech.\ Rept.\ 42 

\reference Liu, Z.-Y., 1987, MMA Memo 41

\reference Matsushita, S., Matsuo, H., Pardo, J. R., \& Radford, S. J. E., 1999, PASJ 51, 603

\reference Matsushita, S., Matsuo, H., Sakamoto, A., \& Pardo, J. R., 
2000 Proc.\ SPIE 4015, 378

\reference McKinnon, M., 1987, MMA Memo 40

\reference Pardo, J. R., Cernicharo, J., \& Serabyn, E., 2001, 
IEEE Trans.\ Ant.\ Prop.\ in press

\reference Radford, S. J. E., \& Holdaway, M. A., 1998, Proc.\ SPIE 3357, 486

\reference Radford, S. J. E., \& Chamberlin, R. A., 2000, ALMA Memo 334

\reference Wild, W., \& Payne, J., 2001, ALMA Project Book Chapter 5

\clearpage

% Table 1
\begin{table}
\begin{center}
\caption{\strut Simultaneous (Paired) Data}
\begin{tabular}{lccccl} 
\hline
\strut & & \multicolumn{3}{c}{median}\\
\cline{3-5}
\strut month & $r$ & $\tau_{225}$& $\tau_{220}$& $\tau_{220} - \tau_{225}$& remarks\\
\cline{5-5}
\strut & & Chaj.& Bola& $\tau_{225}$\\
\hline
\strut 1996 July      & 0.77& 0.069& 0.109& $+0.48$& sporadic\\
\strut 1996 October   & 0.38& 0.058& 0.068& $+0.41$& sporadic\\
\strut 1996 November  & 0.24& 0.046& 0.080& $+0.43$& poor correlation\\
\strut 1996 December  & 0.43& 0.061& 0.066& $+0.04$& sporadic\\
\\
\strut 1997 June      & 0.60& 0.038& 0.039& $-0.08$& sporadic\\
\strut 1997 July      & 0.30& 0.079& 0.078& $-0.07$& sporadic\\
\strut 1997 September & 0.44& 0.115& 0.127& $+0.09$& sporadic\\
\\
\strut 1999 June      & 0.95& 0.038& 0.047& $+0.27$\\ 
\strut 1999 July      & 0.92& 0.038& 0.048& $+0.25$\\
\strut 1999 August    & 0.93& 0.036& 0.046& $+0.24$\\
\strut 1999 September & 0.94& 0.045& 0.056& $+0.19$\\
\strut 1999 October   & 0.90& 0.053& 0.060& $+0.10$\\
\strut 1999 November  & 0.89& 0.038& 0.046& $+0.16$\\
\strut 1999 December  & 0.93& 0.039& 0.045& $+0.10$\\
\\
\strut 2000 March     & 0.69& 0.089& 0.110& $+0.07$\\
\strut 2000 April     & 0.83& 0.056& 0.073& $+0.30$\\
\strut 2000 May       & 0.66& 0.061& 0.125& $+0.85$\\
\strut 2000 June      & 0.95& 0.041& 0.060& $+0.46$\\
\strut 2000 July      & 0.90& 0.027& 0.044& $+0.55$\\
\strut 2000 September & 0.85& 0.029& 0.044& $+0.44$\\
\strut 2000 October   & 0.88& 0.043& 0.060& $+0.35$\\
\strut 2000 November  & 0.85& 0.035& 0.053& $+0.44$\\
\strut 2000 December  & 0.78& 0.080& 0.101& $+0.21$\\
\\
\strut 1999 June--2000 December & 0.91& 0.043& 0.054& $+0.23$& 60 min medians\\
\\
\strut 2001 April--May & 0.97& & & $-0.03$& side-by-side comparison\\
\hline
\end{tabular}
\end{center}
\end{table}


\clearpage
% Table 2

\begin{table}
\begin{center}
\caption{\strut Integration Time Ratios}
\begin{tabular}{crrrrrcc}
\hline
\multicolumn{1}{c}{\strut $\nu$}& 
 \multicolumn{1}{c}{$T_{\rm rec}$}& 
 \multicolumn{1}{c}{$a$}& 
 \multicolumn{1}{c}{$b$}& 
 \multicolumn{1}{c}{$\tau_1$}& 
 \multicolumn{1}{c}{$\tau_2$}& 
 \multicolumn{2}{c}{$t_1/t_2$}\\
\cline{7-8}
\multicolumn{1}{c}{\strut [GHz]}& \multicolumn{1}{c}{[K]}& &&&&  \multicolumn{1}{c}{zenith}& \multicolumn{1}{c}{$A=1.1$}\\ 
\hline
\phantom{0}220	&	55&	\multicolumn{1}{c}{---}	&	\multicolumn{1}{c}{---}	&	0.045	&	0.036	&	\phantom{0}1.1	&\phantom{0}1.1\\	
\phantom{0}345	&	83&	3.65	& $-0.008$	&	0.16\phantom{0}	&	0.12\phantom{0}	&	\phantom{0}1.2	&	\phantom{0}1.2\\	
\phantom{0}410	&	98&	7.53	& $-0.017$	&	0.32\phantom{0}	&	0.25\phantom{0}	&	\phantom{0}1.4	&	\phantom{0}1.4\\	
\phantom{0}492	&	118&	23.6\phantom{0}	& $+0.19\phantom{0}$	&	1.25\phantom{0}	&	1.04\phantom{0}	&	\phantom{0}1.7	&	\phantom{0}1.8\\	
\phantom{0}675	&	162&	22.4\phantom{0}	& $-0.02\phantom{0}$	&	0.99\phantom{0}	&	0.79\phantom{0}	&	\phantom{0}1.7	&	\phantom{0}1.8\\	
\phantom{0}691	&	166&	26.4\phantom{0}	& $-0.06\phantom{0}$	&	1.13\phantom{0}	&	0.89\phantom{0}	&	\phantom{0}1.8	&	\phantom{0}1.9\\	
\phantom{0}809	&	194&	33.4\phantom{0}	& $-0.03\phantom{0}$	&	1.47\phantom{0}	&	1.17\phantom{0}	&	\phantom{0}2.0	&	\phantom{0}2.2\\	
\phantom{0}875	&	210&	24.2\phantom{0}	& 0\phantom{.000}		&	1.09\phantom{0}	&	0.87\phantom{0}	&	\phantom{0}1.7	&	\phantom{0}1.8\\	
\phantom{0}922	&	221&	72\phantom{.00}	& $+0.02\phantom{0}$	&	3.4\phantom{00}	&	2.6\phantom{00}	&	\phantom{0}3.8	&	\phantom{0}4.3\\	
\phantom{0}937	&	225&	43.9\phantom{0}	& $-0.02\phantom{0}$	&	1.96\phantom{0}	&	1.56\phantom{0}	&	\phantom{0}2.4	&	\phantom{0}2.6\\	
1035&	248&	123\phantom{.00}	& $-0.8\phantom{00}$	&	4.7\phantom{00}	&	3.6\phantom{00}	&	\phantom{0}9.3	&	11.6\\	
1350&	324&	115\phantom{.00}	&	\multicolumn{1}{c}{---}	&	5.2\phantom{00}	&	4.1\phantom{00}	&	\phantom{0}8.0	&	\phantom{0}9.8\\	
1500&	360&	101\phantom{.00}	&	\multicolumn{1}{c}{---}	&	4.5\phantom{00}	&	3.6\phantom{00}	&	\phantom{0}6.2	&	\phantom{0}7.5\\
\hline
\end{tabular}
\end{center}
\break
\strut Optical depth 
regressions [$\tau(\nu) = a(\nu)\, \tau_{220} + b(\nu)$]
from Matsushita et al.\ 2000. 
Other conditions: ALMA receiver goals,
$T_{\rm rec} = 5 h \nu / k$; median ambient air temperature
at Chajnantor, $T_{\rm atm} = 270$\,K; 
first quartile zenith optical depth at Chajnantor,
$\tau_2(225\,{\rm GHz}) = 0.036$;
typical normalized optical depth difference,
$(\tau_1-\tau_2)/\tau_2 = 0.25$;
zenith and 
$A = 1.1$, which is the median for 
transit observations of uniformly distributed 
sources at $z<60^\circ$. 
\end{table}
	

 


\clearpage

\begin{figure}[p]
\begin{center}
\leavevmode
\psfig{file=compare-225.ps,angle=-90,width=5.5in}
\end{center}
\caption{
Cumulative distributions of the 225\,GHz
zenith optical depth ($\tau_{225}$) measured
at Chajnantor, at Mauna Kea (CSO), and at the South Pole
(after Radford \& Chamberlin 2000).
}
\label{fig:cdf}
\end{figure}

%==========
\clearpage

\begin{figure}[p]
\begin{center}
\leavevmode
\psfig{file=1999-07-chaj-bola-time.ps,height=6.0in,bbllx=49bp,bblly=67bp,bburx=547bp,bbury=732bp,clip=}
\end{center}
\caption{
Zenith optical depth measured at Chajnantor ($\tau_{225}$) and
at Pampa la Bola ($\tau_{220}$) during 1999 July.
}
\label{fig:time_199907}
\end{figure}

\clearpage

\begin{figure}[p]
\begin{center}
\leavevmode
\psfig{file=1999-07-chaj-bola-stats.ps,height=6.0in,bbllx=64bp,bblly=40bp,bburx=575bp,bbury=565bp,clip=}
\end{center}
\caption{
Time synchronized (paired) measurements of atmospheric transparency  
during 1999 July.
{\it Left:}\/ Cumulative distributions ({\it top}\/) and correlation ({\it bottom}\/) of
zenith optical depths, $\tau_{225}$ (Chajnantor) and $\tau_{220}$ (Pampa la Bola).
{\it Right:}\/ Cumulative distribution ({\it top}\/) and correlation ({\it bottom}\/) of
normalized differences, $[\tau_{220}({\rm Bola}) - \tau_{225} ({\rm Chaj.})]/\tau_{225}$.
}
\label{fig:stats_199907}
\end{figure}

%==========
\clearpage

\begin{figure}[p]
\begin{center}
\leavevmode
\psfig{file=1999-10-chaj-bola-time.ps,height=6.0in,bbllx=49bp,bblly=67bp,bburx=547bp,bbury=732bp,clip=}
\end{center}
\caption{
Zenith optical depth measured at Chajnantor ($\tau_{225}$) and
at Pampa la Bola ($\tau_{220}$) during 1999 October.
}
\label{fig:time_199910}
\end{figure}

\clearpage

\begin{figure}[p]
\begin{center}
\leavevmode
\psfig{file=1999-10-chaj-bola-stats.ps,height=6.0in,bbllx=64bp,bblly=40bp,bburx=575bp,bbury=565bp,clip=}
\end{center}
\caption{
Time synchronized (paired) measurements of atmospheric transparency  
during 1999 October.
{\it Left:}\/ Cumulative distributions ({\it top}\/) and correlation ({\it bottom}\/) of
zenith optical depths, $\tau_{225}$ (Chajnantor) and $\tau_{220}$ (Pampa la Bola).
{\it Right:}\/ Cumulative distribution ({\it top}\/) and correlation ({\it bottom}\/) of
normalized differences, $[\tau_{220}({\rm Bola}) - \tau_{225} ({\rm Chaj.})]/\tau_{225}$.
}
\label{fig:stats_199910}
\end{figure}

%==========
\clearpage

\begin{figure}[p]
\begin{center}
\leavevmode
\psfig{file=2000-10-chaj-bola-time.ps,height=6.0in,bbllx=49bp,bblly=67bp,bburx=547bp,bbury=732bp,clip=}
\end{center}
\caption{
Zenith optical depth measured at Chajnantor ($\tau_{225}$) and
at Pampa la Bola ($\tau_{220}$) during 2000 October.
}
\label{fig:time_200010}
\end{figure}

\clearpage


\begin{figure}[p]
\begin{center}
\leavevmode
\psfig{file=2000-10-chaj-bola-stats.ps,height=6.0in,bbllx=64bp,bblly=40bp,bburx=575bp,bbury=565bp,clip=}
\end{center}
\caption{
Time synchronized (paired) measurements of atmospheric transparency  
during 2000 October.
{\it Left:}\/ Cumulative distributions ({\it top}\/) and correlation ({\it bottom}\/) of
zenith optical depths, $\tau_{225}$ (Chajnantor) and $\tau_{220}$ (Pampa la Bola).
{\it Right:}\/ Cumulative distribution ({\it top}\/) and correlation ({\it bottom}\/) of
normalized differences, $[\tau_{220}({\rm Bola}) - \tau_{225} ({\rm Chaj.})]/\tau_{225}$.
}
\label{fig:stats_200010}
\end{figure}

%==========
\clearpage

\begin{figure}[p]
\begin{center}
\leavevmode
\psfig{file=boxcar-stats.ps,height=6.0in,bbllx=64bp,bblly=40bp,bburx=575bp,bbury=565bp,clip=}
\end{center}
\caption{
Hourly median measurements of atmospheric transparency for 
1999 June through 2000 December.
{\it Left:}\/ Cumulative distributions ({\it top}\/) and correlation ({\it bottom}\/) of
zenith optical depths, $\tau_{225}$ and $\tau_{220}$.
{\it Right:}\/ Cumulative distribution ({\it top}\/) and correlation ({\it bottom}\/) of
normalized differences, $(\tau_{220} - \tau_{225} )/\tau_{225}$.
}
\label{fig:stats_boxcar}
\end{figure}


%==========
\clearpage

\begin{figure}[p]
\begin{center}
\leavevmode
\psfig{file=2001-04-chaj-comp-time.ps,height=6.0in,bbllx=49bp,bblly=67bp,bburx=547bp,bbury=732bp,clip=}
\end{center}
\caption{
Zenith optical depth measured at 225\,GHz ($\tau_{225}$) and
at 220\,GHz ($\tau_{220}$) during side-by-side comparison
measurements at Chajnantor during 2001 April--May.
}
\label{fig:time_200104}
\end{figure}

\clearpage

\begin{figure}[p]
\begin{center}
\leavevmode
\psfig{file=2001-04-chaj-comp-stats.ps,height=6.0in,bbllx=64bp,bblly=40bp,bburx=575bp,bbury=565bp,clip=}
\end{center}
\caption{
Time synchronized (paired) measurements of atmospheric transparency  
during side-by-side comparison
measurements at Chajnantor during 2001 April--May.
{\it Left:}\/ Cumulative distributions ({\it top}\/) and correlation ({\it bottom}\/) of
zenith optical depths, $\tau_{225}$ and $\tau_{220}$.
{\it Right:}\/ Cumulative distribution ({\it top}\/) and correlation ({\it bottom}\/) of
normalized differences, $(\tau_{220} - \tau_{225} )/\tau_{225}$.
}
\label{fig:stats_200104}
\end{figure}

\end{document}

