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Otárola, A.;Hiriart, D.;Pérez-León, J. E.
STATISTICAL CHARACTERIZATION OF PRECIPITABLE WATER VAPOR AT SAN
PEDRO MARTIR SIERRA IN BAJA CALIFORNIA
Revista Mexicana de Astronomía y Astrofísica, Vol. 45, Núm. 2, 2009, pp. 161-169
Universidad Nacional Autónoma de México
México
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© Copyright 2009: Instituto de Astronomía, Universidad Nacional Autónoma de México
Revista Mexicana de Astronom´ıa y Astrof´ısica, 45, 161–169 (2009)
STATISTICAL CHARACTERIZATION OF PRECIPITABLE WATER
VAPOR AT SAN PEDRO MARTIR SIERRA IN BAJA CALIFORNIA
A. Ot´arola,
1
D. Hiriart,
2
and J. E. P´erez-Le´on
2
Received 2009 April 16; accepted 2009 June 23
RESUMEN
Presentamos datos del vapor de agua precipitable durante 2006 para la Sierra
de San Pedro M´artir obtenidos de mediciones de la emisi´on atmosf´erica como
funci´on del ´angulo de elevaci´on por un radi´ometro operando a la frecuencia de
210 GHz. Las mediciones de este radi´ometro se combinan con valores de tempe-
ratura y presi´on atmosf´erica a nivel del suelo en el sitio para determinar una relaci´on
matem´atica para la conversi´on de la opacidad atmosf´erica al cenit a 210 GHz y la
columna de vapor de agua precipitable para San Pedro M´artir. Los datos del vapor
de agua precipitable se analizan estad´ısticamente para conocer su funci´on de den-
sidad de probabilidad y su distribuci´on acumulativa, as´ı como para determinar el
n´umero de horas continuas al a˜no en que el vapor de agua precipitable permanece
por debajo de los umbrales de 1 mm, 2 mm y 3 mm. Esta informaci´on es de inter´es
para evaluar el desempe˜no de telescopios operando desde la regi´on del ´optico hasta
longitudes de onda milim´etricas en este sitio.
ABSTRACT
We present time series of precipitable water vapor (PWV) for San Pedro
Martir Sierra in 2006, obtained from measurements of atmospheric emission as a
function of elevation angle from a 210 GHz tipping radiometer. These radiometric
measurements are employed together with collocated surface temperature and pres-
sure data to determine a mathematical relationship for the conversion of 210 GHz
zenith optical depth to PWV in the atmospheric column for San Pedro Martir.
The PWV time series are statistically analyzed to gain insights on its probability
density function and cumulative distributions, as well as to learn the number of con-
tinuous hours over a year that the PWV remains below given thresholds, namely
1 mm, 2 mm, and 3 mm. This information is of interest to evaluate the expected
performance of telescopes operating from optical to millimeter wavelengths at this
site.
Key Words: atmospheric effects — site testing
1. INTRODUCTION
The amount of integrated water vapor in the at-
mospheric column is one of many relevant parame-
ters in the determination of the suitability of a site
for the deployment and operation of an astronomi-
cal observatory. The transparency of the atmosphere
to the propagation of electromagnetic signals of cos-
mic origin, for a given level of Precipitable Water
Vapor (PWV) in the atmosphere depends strongly
on the wavelength of the propagating signals. Fig-
1
TMT Observatory Corporation, Pasadena, CA, USA.
2
Instituto de Astronom´ıa, Universidad Nacional Aut´o-
noma de M´exico, Ensenada, B. C., Mexico.
ures 1 and 2 show the atmospheric transmission in
the near infrared (NIR) spectrum as a function of
wavelength, and in the radio spectrum as a func-
tion of frequency, respectively. Figure 1 is a high-
resolution spectrum created from transmission data
available for the Kitt Peak observatory and described
in Hinkle, Wallace, & Livingston (2003). Figure 2
was produced with transmission data generated by
the program am using a multi-layer, line-by-line, at-
mospheric model (Paine 2004) for 1 mm of PWV in
the atmospheric column, and using typical parame-
ters (surface temperature, surface pressure, and tem-
perature lapse rate) for the San Pedro Martir loca-
tion.
161
© Copyright 2009: Instituto de Astronomía, Universidad Nacional Autónoma de México
162 OT
´
AROLA, HIRIART, & P
´
EREZ-LE
´
ON
Fig. 1. Example of the measured atmospheric transmis-
sion at Kitt Peak (at standard atmospheric conditions)
for the near infrared.
Some of the opaque bands in the spectra shown
in Figures 1 and 2 are due to absorption of elec-
tromagnetic signal energy by molecules of water va-
por (H
2
O) in the atmosphere. Additional absorption
bands are attributed to absorption by CO
2
, O
2
, O
3
,
N
2
O, and other active constituents in the earth’s at-
mosphere.
For the performance of an astronomical obser-
vatory for conducting research in the infrared and
millimeter bands not only the absolute amount of
PWV in the atmospheric column is important, its
temporal variability within the span of a given as-
tronomical research program and over the course of
the observing night are equally important.
This study focuses on the statistical characteriza-
tion of PWV time series estimated for the San Pedro
Martir site through 2006. However, it also includes
the evaluation of statistical results from previous
studies available in the scientific literature covering
the period 1995–2002. § 1 describes the basic observ-
ables given by the atmospheric thermal emission de-
tected by a 210 GHz tipper radiometer as function of
elevation angle (airmass), and its conversion to opti-
cal depth at zenith using the Langley plot approach.
§ 2 explains the strategy developed to take optical
depth time series and collocated surface weather pa-
rameters to derive an empirical model useful to es-
timate PWV from optical depth measurements. § 3
provides the results of the statistic characterization
of the PWV time series. § 4 provides the conclu-
sions from the analysis of the PWV data for the San
Pedro Martir Sierra site and some recommendations
for future work.
0 100 200 300 400 500 600 700 800 900 1000
0
0.2
0.4
0.6
0.8
1
Frequency, GHz
Transmission
H
2
O H
2
O H
2
O H
2
O
O
2
O
2
Fig. 2. Modeled atmospheric transmission at San Pedro
Martir for 3 mm (solid line) and 1 mm (dashed line)
of PWV, surface temperature of 280 K, surface pressure
of 730 hPa, temperature lapse rate of −6.5 K/km, and
water vapor scale height of 1.8 km.
2. BASIC OBSERVABLES AND
DETERMINATION OF OPTICAL DEPTH
TIME SERIES
Time series of atmospheric thermal emission at
the San Pedro Martir site have been generated
with the help of a tipping radiometer operating at
215 GHz in the period 1992 until 1994. A technical
description of the instrument, logic of the data re-
duction process to obtain zenith optical depths time
series and results of the observations through 1992
were presented by Hiriart et al. (1997). The first
generation 215 GHz tippers were modified to make
them more reliable, capitalizing on the availability
of mixers and and Gunn oscillators that yield lower
overall instrumental noise temperature working at
210 GHz. A description of the changes introduced
in the tipper radiometers and time series of optical
depths at 210 GHz observed in 1999 is included in
Hiriart (2003a).
In a succinct way, optical depth can be obtained
from measurements of atmospheric emission at dif-
ferent elevation angles through (Hiriart et al. 1997)
ln(V
REF
−V
SKY
(z)) = −τ
o
sec(z)+ln(gηT
ATM
) , (1)
where the basic observables V
REF
and V
SKY
(z) are
the voltage measured by feeding the tipper radiome-
ter with the signal from a reference load at room
temperature, and the voltage measured from the sky
signal at a zenith angle z, respectively.
Figure 3, known to atmospheric scientists as the
Langley plot, shows an example of a full skydip ob-
© Copyright 2009: Instituto de Astronomía, Universidad Nacional Autónoma de México
PWV STATISTICS AT SAN PEDRO MARTIR 163
Fig. 3. Langley plot to show ln(V
REF
− V
SKY
(z)) as a
function of airmass z for a full skydip.
servation. Circles show the natural log of the differ-
ence between the mean values of V
REF
and V
SKY
(z),
the vertical bars correspond to the ±1σ
obs
in the
ln(V
REF
− V
SKY
(z)) quantity. At each airmass, the
radiometer measures 30 times the values of the sky
and the reference load signals, and delivers the mean
value of the observable V
REF
and V
SKY
(z) and its
standard deviation σ
REF
and σ
SKY(z)
, respectively.
Following the propagation of the errors on the basic
observables, we obtain
σ
obs
=
1
V
REF
− V
SKY(z)
(σ
2
V
REF
+ σ
2
V
SKY
(z)
)
1/2
. (2)
The dashed line in Figure 3 corresponds to the
linear polynomial function that best fits the observa-
tions, in a weighted least-squares sense. The solution
of this fit is given by
X = (G
T
W
obs
G)
−1
G
T
W
obs
Y , (3)
where X is a column matrix of size 2 with the
first element being the solution for τ
o
(slope) and
ln(gηT
ATM
) (intercept), respectively. The intercept
is a measure of a quantity that relates to the gain
of the radiometer system (Hiriart et al. 1997). The
G matrix array has two columns, the first column is
1 and the second column corresponds to the magni-
tude of sec(z) with a total of eight rows, one for
each airmass observed. The W
obs
correspond to
the statistical weights for the observable quantity
ln(V
REF
−V
SKY
(z)) and are defined as W
obs
= 1/σ
2
obs
In this way, the less disperse measurements have
higher relevant weights.
The covariance matrix of the model parameters,
Cov
x
, is given by
Cov
x
= (G
T
G)
−1
G
T
Cov
obs
((G
T
G)
−1
G
T
)
T
, (4)
where Cov
obs
is the covariance matrix of the observ-
ables. The main diagonal of the covariance matrix,
Cov
x
, includes the variance for the model parame-
ters τ
o
and ln(gηT
ATM
).
The 210 GHz radiometer data at San Pedro Mar-
tir can be used to produce a determination of zenith
optical depth with a time resolution of about six min-
utes.
3. OPTICAL DEPTH AND PRECIPITABLE
WATER VAPOR
At radio wavelengths, the atmospheric trans-
parency is dominated by absorption of water va-
por –because of its permanent electric dipole– and
molecular oxygen –because of its permanent mag-
netic dipole– as shown in Figure 2. A line-by-
line, multi-layer radiative transfer model, such as am
(Paine 2004), ATM (Pardo, Cernicharo, & Serabyn
2001), MODTRAN (Berk, Bernstein, & Robertson
1989), or any other equivalent model, together with
known vertical profiles of temperature (T ), atmo-
spheric pressure (P ), and water vapor density (ρ
W
),
can be used to compute the atmospheric optical
depth (τ
o
) at a given frequency. An accurate de-
termination of τ
o
implies a corresponding accurate
knowledge of the state of the atmosphere along the
vertical axis at the site of interest; this is possi-
ble when data from vertical atmospheric soundings
are available. Similarly, if the total optical depth
is known the integrated water vapor (IWV) in the
atmospheric column can be obtained through an in-
version process. However, this process is rather time-
consuming since the radiative transfer model has to
be run iteratively by varying the IWV until the mod-
eled and observed optical depths match within ac-
ceptable tolerances.
For this study, we obtain time series of basic ob-
servables in the period of time 2004 to 2006 from
the SPM radiometer. Unfortunately, the time series
show gaps of varying length in time (see Figure 4)
and this prevents us from having a good coverage
of all seasons through these years. The year with
the most data is 2006 and an approach was devel-
oped in this study to use the data from years 2004
and 2005 to fill some of the gaps in the data se-
ries for 2006. This approach is valid under the as-
sumption of stable climatology in the period 2004-
2006, supported by a quick analysis of the El Ni˜no
3 index
3
time series available from the NOAA Cli-
mate Prediction Center at http://www.cdc.noaa.
gov/ClimateIndices/List/.
3
This corresponds to the sea surface temperature on the
Eastern Tropical Pacific (5S-5N;150W-90W).
© Copyright 2009: Instituto de Astronomía, Universidad Nacional Autónoma de México
166 OT
´
AROLA, HIRIART, & P
´
EREZ-LE
´
ON
Fig. 8. PWV probability density function (PDF) and cu-
mulative distribution function (CDF) for nighttime (left)
and daytime (right) of the SY2006 database.
Fig. 9. PWV statistics at the San Pedro Martir Sierra,
1999. First quartile (triangles), monthly median values
(ovals), and third quartile (squares).
optical depth statistics from the paper of Hiriart
(2003b) for the nighttime and daytime at San Pe-
dro Martir, respectively. The gaps in these figures
correspond to times when measurements of 210 GHz
optical depth were not available. The average of the
mean values reaches 2.9 mm and 3.3 mm for the
nighttime and daytime statistics in the 1995–2003
period, respectively.
The PWV time series in Figure 9 and the statis-
tics shown in Figures 10 and 11 are useful to show
that San Pedro Martir is characterized by a relatively
dry period covering October through May and a wet
period from June through September in the present
Fig. 10. Monthly nighttime mean PWV at the San Pedro
Martir Sierra.
Fig. 11. Monthly daytime mean PWV at the San Pedro
Martir Sierra.
data. The wet period might be attributed in part
to the west reach of the North American Monsoon
(NAM) and the effect of moisture advection as result
of tropical storms and cyclonic activity originating
on the east Pacific along the southern coast of Mex-
ico.
In developing a site for astronomical research it
is especially important to establish the relative sta-
bility of atmospheric conditions over time intervals
representative of a typical observing sequence. In
this regard, the SY2006 PWV data series were ana-
lyzed to look for the total number of hours that the
PWV remains below a given threshold. The results
of this analysis are shown in Table 1. Columns 2 & 3
© Copyright 2009: Instituto de Astronomía, Universidad Nacional Autónoma de México
PWV STATISTICS AT SAN PEDRO MARTIR 167
TABLE 1
NUMBER OF HOURS THE PWV IS BELOW A GIVEN THRESHOLD AT
SAN PEDRO MARTIR BASED ON THE SY2006 DATABASE
PWV Threshold Time with at Percent of the 6 Total Time Percent of the
at least 2 SY2006 database with PWV below SY2006 database
continuous hours 7,276 total hours given threshold 7,276 total hours
below threshold of available data of available data
(mm) (hours) (%) (hours) (%)
0.7 34.9 0.5 48.3 0.7
1.0 195.4 2.7 248.2 3.4
2.0 1529.4 21.0 1653.7 22.7
3.0 2966.0 40.8 3157.6 43.4
4.0 3987.4 54.8 4166.0 57.3
5.0 4671.4 64.2 4800.5 66.0
6.0 5095.6 70.0 5248.7 72.1
7.0 5394.7 74.1 5523.9 75.9
8.0 5595.1 76.9 5725.4 78.7
9.0 5770.6 79.3 5894.3 81.0
10.0 5919.8 81.4 6070.3 83.4
of Table 1 show the number of hours, and its percent-
age, of the data in SY2006 database that the PWV
remains for at least two hours continuously below the
threshold shown in the first column. Columns 4 &
5 show the total number of hours that the PWV re-
mained below the given threshold with no restriction
of a minimum of two consecutive hours.
The restriction of looking for at least two hours
of PWV to remain below a given threshold has to do
with the fact that, in a flexible scheduling operation
of the telescope observing time, a reasonable time is
necessary to set up the whole system (software and
hardware) for a change in the observing program.
On average, in 2% of the time the PWV is not
stable enough to remain at least two consecutive
hours below the given threshold, as it can be inferred
from the analysis of the information in Columns 3
and 5 in Table 1. Besides, from Table 1, it can be in-
ferred that for about 20% of the time in the year the
PWV values are larger than 10 mm, which amounts
to about 2 months corresponding to the summer sea-
son.
Figure 12 shows the number of hours, with a min-
imum of 2 continuous hours, that the PWV at San
Pedro Martir remains below the thresholds of 1 mm,
2 mm, and 3 mm through the year. The gaps cen-
tered around day of the year 80 and 140 are due to
lack of data, but the gap from days 190 until 260 are
Fig. 12. Total number of continuous hours, with a min-
imum of 2 continuous hours, that the PWV at San Pe-
dro Martir Sierra remains below the thresholds of 1 mm
(top), 2 mm (middle), and 3 mm (bottom) as function
of day of the year.
due to the very wet conditions of the summer at San
Pedro Martir and at no time the PWV goes below 3
mm for at least two continuous hours.
5. CONCLUSIONS AND FUTURE WORK
Time series of optical depth observed at the San
Pedro Martir Sierra with the help of a 210 GHz tip-
ping radiometer have been analyzed. The data in-
© Copyright 2009: Instituto de Astronomía, Universidad Nacional Autónoma de México
168 OT
´
AROLA, HIRIART, & P
´
EREZ-LE
´
ON
clude measurements performed in 2004, 2005, and
2006. The atmospheric conditions through this pe-
riod of time are considered rather normal and rep-
resentative of the climatology of the site. The data
through these years show gaps, some of them quite
large. The data from years 2004 and 2005 were used
to fill up the gaps in the data series of 2006, in order
to obtain a more representative vision of the recent
time seasons at this site.
A small fraction of the optical depth data se-
ries in this synthetic database (SY2006) was used,
together with collocated surface data (temperature
and pressure) and with the help of the program am
of a radiative transfer model, to derive a simple re-
lationship to convert optical depths at 210 GHz to
an equivalent amount of precipitable water vapor in
the atmospheric column. This relationship, shown in
Equation 5, produces PWV values which are about
5% smaller in magnitude than a similar relationship
derived by Hiriart & Salas (2007). It is important to
notice that the surface pressure of 625 mb listed by
Hiriart & Salas (2007) in their Table 1 is too low a
pressure for San Pedro Martir. In spite of this low
pressure, the results in Hiriart & Salas (2007) are
an indication that the pressure is affected by a typo
error and the value used in that study was probably
more like 725 mbar.
The PWV-optical-depth relationship found in
this study was applied to the SY2006 database as
well as statistical results known for the San Pedro
Martir Sierra from other studies available in the sci-
entific literature for the years 1999 (in a single study)
and for the years 1995 to 2002 in another study. The
results show that the overall mean value of PWV
through the years at the San Pedro Martir Sierra is
about 3 mm.
San Pedro Martir Sierra is characterized by a
winter, spring and part of the fall season with rel-
atively low values of PWV in the atmospheric col-
umn, with a median value of no more than 2.5 mm.
However, it is also affected by a wet summer with
at least two months of the year with PWV values
larger than 10 mm. This wet period corresponds to
that characterized by the reach of the North Ameri-
can Monsoon and the occasional incursion of tropical
storms and cyclonic activity in general.
Regarding the persistence of the PWV series be-
low given thresholds, of great importance for the
development of astronomical observing programs, it
was found that during about 20% and 40% of the
time through the SY2006 database the PWV re-
mains continuously below 2 mm and 3 mm for at
least two uninterrupted hours, respectively. Con-
cerning the very dry periods, the site remains be-
low 1 mm of PWV for at least two continuous hours
no more than 3% of the time. Hiriart (2003b), has
found the persistence of PWV to stay below 1 mm
(estimated from 210 GHz optical depth time series)
to be 4% and 10% of the year for 1994 and 1999, re-
spectively. The lower value of 3% found in this study
from the analysis of the SY2006 database might be
due to the fact there are gaps in the data series
through winter time which correspond to the low
PWV values season.
For future work it would be advisable to carry
on a program for the vertical sounding of the at-
mosphere at San Pedro Martir by launching radio-
probes. The information gathered in this way would
help to better characterize the temperature lapse
rate, water vapor scale height, and its variations
through the seasons. It will also provide information
on the existence and strength of temperature inver-
sion layers and on the advection of water vapor into
the different layers of the atmosphere. Ultimately,
high vertical resolution soundings can provide useful
information to gain insight on the atmospheric tur-
bulence and wind profile which are also very relevant
parameters affecting the performance of optical and
infrared telescopes.
The authors gratefully acknowledge the support
of the TMT partner institutions. They are the Asso-
ciation of Canadian Universities for Research in As-
tronomy (ACURA), the California Institute of Tech-
nology, and the University of California. This study
was supported as well by the Gordon and Betty
Moore Foundation, the Canada Foundation for Inno-
vation, the Ontario Ministry of Research and Innova-
tion, the National Research Council of Canada, the
Natural Sciences and Engineering Research Coun-
cil of Canada, the British Columbia Knowledge De-
velopment Fund, the Association of Universities for
the Research of Astronomy (AURA), and the U.S.
National Science Foundation. The authors appreci-
ate the support from Dr. Matthias Sch¨ock and Dr.
Tony Travouillon, and thank an anonymous reviewer
whose comments and suggestions greatly helped to
improve the manuscript.
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