\documentclass[journal]{rmaa}


\newcommand{\casitiny}{\fontsize{6}{7}\selectfont}


\title{Atmospheric Aerosol Variability over the Region\\ of San Pedro M\'artir from MODIS Data}


\author{Mario R. Araiza Quijano and Irene Cruz-Gonz\'alez\affil{Instituto de Astronom\'{\i}a, Universidad Nacional Aut\'onoma de M\'exico, Mexico}}


\shortauthor{Araiza Quijano \& Cruz-Gonz\'alez}

\shorttitle{Atmospheric Aerosol over San Pedro M\'artir}


\listofauthors{M.~R.~Araiza~Quijano \& I.~Cruz-Gonz\'alez}

\indexauthor{Araiza Quijano, M.~R.}
\indexauthor{Cruz-Gonz\'alez, I.}


\fulladdresses{
\item Mario R. Araiza Quijano and Irene Cruz-Gonz\'alez: Instituto de Astronom\'ia, Universidad Nacional Aut\'onoma de M\'exico, Apdo. Postal 70--264, 
04510 M\'exico, D. F., Mexico (maraizaq@astroscu.unam.mx, irene@astro.unam.mx).}


\SetYear{2011}
\ReceivedDate{2010 June 23}
\AcceptedDate{2011 August 15}


\abstract{A study is presented of the atmospheric aerosol optical thickness (AOT) in the astronomical site of San Pedro M\'artir, B. C., Mexico, 
during the 2000--2008 period. The AOT measurements were made by the {\it Moderate Resolution Imaging Spectroradiometer} (MODIS) instrumentation, 
on board of the NASA {\it Aqua} and {\it Terra} satellites. Characteristic seasonal values were identified, showing a higher atmospheric 
transparency in autumn. The best conditions for atmospheric transparency occur in October and November. The annual behavior of MODIS AOT yields 
average values for SPM during the years 2000--2008 of $0.147 \pm 0.103$, $0.128 \pm 0.090$, $0.115 \pm 0.081$, $0.087 \pm 0.066$ at 4700, 5500, 
6600 and 21300~\AA, respectively. We used these mean values to analyze the wavelength dependence and found aerosol scattering slopes 
$\alpha_\mathrm{OIR} \sim 0.31 \pm 0.06$, and a relation $\tau_\lambda \sim 0.0061\lambda^{-0.31}$, for aerosol scattering over the San Pedro M\'artir 
location.\medskip}


\resumen{Se presenta un estudio del espesor \'optico del aerosol atmosf\'erico (AOT por sus siglas en ingl\'es) en el sitio astron\'omico de San 
Pedro M\'artir, B. C., M\'exico durante el periodo 2000--2008. Las mediciones del AOT se realizaron con el instrumento {\it Moderate Resolution 
Imaging Spectroradiometer} (MODIS), a bordo de los sat\'elites {\it Aqua} y {\it Terra} de la NASA. Se han identificado valores caracter\'isticos 
estacionales que muestran un comportamiento de mayor transparencia atmosf\'erica durante el oto\~no. Las mejores condiciones de transparencia 
atmosf\'erica ocurren durante octubre y noviembre. El comportamiento anual durante 2000--2008 del AOT de MODIS da valores promedio de $0.147 \pm 0.103$, 
$0.128 \pm 0.090$, $0.115 \pm 0.081$, $0.087 \pm 0.066$ en 4700, 5500, 6600 and 21300~\AA, respectivamente. Utilizando estos valores promedio se 
analiz\'o la dependencia del AOT con la longitud de onda, y se encontr\'o que $\alpha_\mathrm{OIR} \sim 0.31 \pm 0.06$ y la relaci\'on  
$\tau_\lambda \sim 0.0061 \lambda^{-0.31}$ para dispersi\'on por aerosoles en el sitio de San Pedro M\'artir.\medskip}


\addkeyword{atmospheric effects}
\addkeyword{site testing}


\begin{document}

\maketitle


\section{Introduction}

Until recently, the measurements of the atmospheric opacity of aerosol were obtained on ground-based observing stations as AERONET from NASA, 
that has more than 100 stations distributed around the world. It is not until 2000 and 2002 that the operation of the NASA satellites {\it Terra} 
and {\it Aqua} started, and systematic measurements at different geographic locations of the atmospheric aerosol optical thickness (AOT), among 
many other parameters, were made available. The ambient AOT of different locations around the world have been obtained using these satellites 
and compared to AERONET data in several publications (e.g., Ichoku et al. 2002, 2004; de Meij et al. 2006; Pires, Correia, \& Paixao 2007; Green, 
Kondragunta, \& Ciren 2008; Xia et al. 2008), to study AOT variations.

The characterization of astronomical sites (e.g., Mu\~noz-Tu\~n\'on, Sarazin, \& Vernin 2007; Sch\"ock et al. 2007; Tapia et al. 2007) require 
a detailed and long term testing, in terms both of precision and variability, of a variety of characteristics including fractional cloud cover, 
precipitable water vapor, long-term weather patterns, prevailing winds, atmospheric seeing and turbulence profiles, geologic activity, local 
climate variability, light pollution, among others. Mexico's National Astronomical Observatory (OAN) site is at San Pedro M\'artir (SPM), located 
$31^\circ 02'40''$~N and $115^\circ 28'00''$~W, some 100~km east of the West Coast of Baja California, Mexico. Astronomical characterization studies 
of SPM since the 1980's have been reported in a dedicated volume edited by Cruz-Gonz\'alez, \'Avila, \& Tapia (2003), and in a collection of 
progress reports: Cruz-Gonz\'alez et al. (2004), Tapia, Cruz-Gonz\'alez, \& \'Avila (2007), Tapia et al. (2007).

Among the concepts related to geophysical properties that have been recently introduced in astronomical site testing is the role played by aerosols 
(e.g., Varela et al. 2007; Varela et al. 2008). These authors argue that ambient aerosol content characterization in a site is important because 
aerosols may produce more stable condensation nuclei, delay precipitation and affect extraterrestrial radiation by extinction, absorption, diffusion 
and reflection.

We present a study of the optical depth of the atmospheric aerosol in the SPM astronomical site. The observation period considered corresponds to 
the years 2000 to 2008. The data were obtained from the {\it Moderate Resolution Imaging Spectroradiometer} (MODIS) instrumentation on board the 
NASA satellites {\it Aqua} and {\it Terra}. We studied the seasonal, monthly and annual behavior of the atmosphere aerosol optical thickness, AOT, 
at the wavelengths 470, 550, 660 and 2130~nm. This paper's content is as follows: In \S~2 we present basic observational atmospheric solar radiation 
techniques; followed by a description of the satellites and instrumentation presented in \S~3. The characteristics of the data are given in \S~4 and 
the methodology is described in \S~5, followed by results and analysis description in \S~6. Finally, our conclusions are presented in \S~7.

\vspace{0.2cm}

\section{Observational Atmospheric Solar Radiation Techniques}

Atmospheric solar radiation techniques consider both terrestrial and spatial observations. Terrestrial observations of direct radiation have been 
used to evaluate the optical depth $\tau_\lambda$ of atmospheric aerosols at different wavelengths $\lambda$ of the electromagnetic spectrum, through 
the relation given by Iqbal (1983):
\begin{equation}
I(\lambda) = I_{0}(\lambda) e^{-\tau_\lambda m}\,,
\end{equation}
where $I_\lambda$ is the measured  irradiance (W~m$^{-2}$), $I_{0}(\lambda)$ is the atmospheric top irradiance (W~m$^{-2}$), $\tau_\lambda $ is the optical 
depth (adimensional), $m$ the air mass (adimensional) and $\lambda$ is the wavelength (nm).

On the other hand, spatial observations of reflected solar radiation have been used to evaluate the optical depth $\tau_\lambda$ of atmospheric aerosols 
using sophisticated modeling (e.g., Toon \& Pollack 1976). The details of the algorithm and the theoretical basis of aerosol data retrieval from the 
MODIS Collection 5 data base are presented in Remer et al. (2005) and Remer, Tanr\'e, \& Kaufman (2006). These authors point out that the ambient aerosol 
optical depth (AOD) is proportional to the aerosol total loading in the vertical column. They show that the upward reflectance (normalized solar radiance), 
at the top of the atmosphere (TOA), is a function of successive orders of radiation interactions, within the coupled surface-atmosphere system. The TOA 
angular (for $\theta_0$, $\theta$, and $\phi = $ the solar zenith, view zenith and relative azimuth angles) spectral reflectance given by 
$\rho_\lambda(\theta_0,\theta,\phi)$ at a wavelength $\lambda$ results from the contribution of scattering of radiation within the atmosphere without 
interaction with the surface, known as the ``atmospheric path reflectance'', the reflection of radiation off the surface that is directly transmitted 
to the TOA (``surface function''), and the reflection of radiation from outside the sensor's field of view (``environment function''). They argue that 
if the environment function is neglected, the TOA angular spectral reflectance, $\rho_\lambda^*(\theta_0, \theta, \phi)$ can be approximated by (c.f. 
equation~8 in Remer et al. 2006):
\begin{equation}
\rho_\lambda^*(\theta_0, \theta, \phi) \,=\, \rho_\lambda^a (\theta_0, \theta, \phi) + \frac{F_\lambda(\theta_0) T_\lambda(\theta) \rho_\lambda^s(\theta_0,
\theta, \phi)}{1-s_\lambda \rho_\lambda^s(\theta_0, \theta, \phi)}\,,
\end{equation}
where $\rho_\lambda^a$ is the atmospheric path reflectance, $F_\lambda$ is the normalized downward flux for zero surface reflectance, $T_\lambda$ represents 
the upward total transmission into the satellite field of view, $s_\lambda$ is the atmospheric back-scattering ratios, and $\rho_\lambda^s$ is the angular 
spectral surface reflectance. They show that except for the surface reflectance, each term on the right hand side of this equation is a function of the 
aerosol type and loading, including aerosol optical depth (AOD) and the fine weighting (FW) of the ambient undisturbed aerosol. Assuming that a small set 
of aerosol types and loadings can describe the range of global aerosol, they have obtained a look-up table that contains their simulations of these aerosol 
conditions. The goal of their algorithm is to use this look-up table (c.f. their \S~4.3) to determine the conditions that best mimic the MODIS-observed 
spectral reflectance $\rho_\lambda^m$, to retrieve the associated aerosol properties (including AOD and FW). They argue that the difficulty lies in making 
the most appropriate assumptions about both the surface and atmospheric contributions. Remer et al. (2006) detailed in \S~4.3 of their work the strategy, 
formulation and calibration with the AERONET data, and describe in detail the algorithm to obtain the land aerosol optical depth (AOD). They presented 
the surface reflectance assumptions in their \S~4.4, followed by the retrieval algorithm in \S~4.5. From the comparison to AERONET data they demonstrate 
that their algorithm is quite reliable for AOD and FW data from MODIS Collection 5.


\vspace{0.2cm}

\section{Satellites and Instrumentation}

Detailed information on the {\it Terra} and {\it Aqua} multinational projects can be obtained at the NASA Web pages\footnote{\url{http://terra.nasa.gov/} 
and \url{http://aqua.nasa.gov/}, respectively.}.


\subsection{Terra spacecraft}

The NASA satellite {\it Terra}, formerly known as {\it EOS AM-1}, carries a payload of five sensors that study interactions among Earth's atmosphere, 
land, oceans, life and radiant energy (heat and light). Each sensor is designed to meet a wide range of science objectives. Two of the instruments were 
supplied by Canada and Japan. {\it Terra} is in a 100-minute polar orbit 437 miles above Earth, flying in close formation with the photography satellite 
{\it Landsat 7}, which was launched in April 1999. In 2002 {\it Terra} was joined by a complementary satellite, {\it Aqua}, formerly known as {\it EOS PM-1}, 
that crosses over the equator each orbit at a later time. {\it Terra} circles Earth from pole to pole in an orbit that descends across the equator at 
10:30 AM when cloud cover is minimal and its view of the surface is least obstructed. The orbit is perpendicular to the direction of Earth's spin.


\subsection{Terra sensors}

The sensors on {\it Terra} do not actively scan the surface like laser beams or microwave pulses do, rather, they work like a camera. Sunlight reflected 
by Earth, and heat emitted by Earth, pass through the apertures of {\it Terra}'s sensors. That radiant energy is focused on detectors that are sensitive 
to selected regions of the electromagnetic spectrum, ranging from visible to infrared light. The information produced by the detectors is transmitted down 
to Earth and processed by computers into images that people can interpret. {\it Terra} sends down as much as one terabyte of data per day.


%%%%% TABLA 1

\begin{table}[!t]
\vspace{0.1cm}
\centering
\setlength{\tabcolsep}{2.5\tabcolsep}
\tablecols{2}
\caption{Aqua and the A-Train}
\label{tab:aqua}
\begin{tabular}{cc}
\toprule
Satellite & Launch \\
\midrule
{\it Aura}  & 2004 July 15 \\
{\it Aqua}  & 2002 May 4   \\
{\it Terra} & 1999 December 18\\
\bottomrule
\end{tabular}
\vspace{0.3cm}
\end{table}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


The formation of orbiting satellites is referred to as the {\it A-Train}, and the launch dates are resented in Table~1. Together, their overlapping 
radars are providing a more comprehensive picture of weather and climate on global Earth. The {\it A Train} satellites fly in low polar orbits 438 
miles above Earth. They circle Earth 14 times a day. {\it Aqua} crosses the equator at approximately 1:30 AM and 1:30 PM, local time, about 3 hours 
behind {\it Terra}. Due to the narrow field of view of its instruments, it takes about 16 days for {\it Aqua} to map the entire surface of the planet.


%%%%% TABLA 2

\begin{table*}[!t]
\vspace{0.1cm}
\centering
%\setlength{\tablewidth}{0.9\columnwidth}
\tablecols{2}
\setlength{\tabcolsep}{2.5\tabcolsep}
\caption{San Pedro M\'artir Aerosol Optical Thickness (AOT) Data}
\label{tab:spmaerosol}
\small
\begin{tabular}{ll}
\toprule
Source of solar radiation data: & MODIS Aerosol, NASA\\
Satellites: & {\it Aqua} and {\it Terra}\\
Instrument: & Moderate Resolution Imaging Spectroradiometer\\
Site: & San Pedro M\'artir, Baja California, Mexico\\
Location:& \\
~~~Latitude & $31^\circ 02'40''$ North\\
~~~Longitude & $115^\circ 28'00''$ West\\
Elevation: & 2830 m\\
Aerosol optical depth observations (2000--2008): &1078\\
Data Files: & 4008\\
Format: & HDF\\
Product Files: & MOD04${\underline \ \ }$L2\\
Collection: & 5\\
Parameter: & Corrected${\underline \ \ }$Optical${\underline \ \ }$Depth${\underline \ \ }$Land \\
Wavelengths, $\lambda$ (nm): & 470, 550, 660\\
Bandwidth $\Delta\lambda$ (nm): & 20, 20, 50\\
Parameter: & Corrected${\underline \ \ }$Optical${\underline \ \ }$Depth${\underline \ \ }$Land${\underline \ \ }$wav2p1\\
Wavelength: & 2130 nm\\
Bandwidth $\Delta\lambda$ (nm): & 50\\
Re projection: & Geographic\\
Re-projected Files: & 8016\\
Extraction Data Files: & 8016\\
\bottomrule
\end{tabular}
\vspace{0.5cm}
\end{table*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\subsection{Aqua Science Instruments}

Each of the school-bus-sized satellite's six science instruments is designed to monitor a different part of our global plumbing system. The six instruments 
are:

\begin{itemize}
\item Atmospheric Infrared Sounder (AIRS)
\item Advanced Microwave Sounding Unit (AMSU-A)
\item Humidity Sounder for Brazil (HSB)
\item Advanced Microwave Scanning Radiometer for EOS (AMSR-E)
\item Moderate-Resolution Imaging Spectroradiometer (MODIS)
\item Clouds and the Earth's Radiant Energy System (CERES)
\end{itemize}

The data obtained by all these instruments is available in a public database supported by NASA. 


\section{MODIS Data}

The MODIS data was obtained from the NASA public database\footnote{\url{http://modis.gsfc.nasa.gov/}.}. The MODIS Aerosol Product monitors the ambient 
aerosol optical thickness (AOT $\equiv\tau$ in equation~1 above) over the oceans globally and over a portion of the continents. 

We extracted MODIS data for the San Pedro M\'artir, Baja California, Mexico geographic location, to obtain the ambient land aerosol optical thickness 
(AOT). Data were obtained for the period from January 2000 to December 2008 at the four spectrometer wavelengths: 470, 550, 660 and 2130~\AA, since we 
are also interested in the wavelength dependence $\tau_\lambda$. The data characteristics are presented in Table~2. The MODIS photometers channels are 
presented in Table~1 of Remer et al. (2006), we note that the central wavelength and bandwidth (in parenthesis) presented in their table are 466 (20), 
553 (20), 646 (50) and 2119 (50) nm, which are slightly different from the ones in the MODIS Web site.


\section{Methodology}
 
In order to obtain the atmospheric optical thickness (AOT) data of the SPM site at the selected wavelengths (4700, 5500, 6600 y 21300~\AA) a set 
of necessary data processing steps were required. The data were processed as follows.


\subsection{Data files acquisition MOD04}

The data files for the 2000--2008 period were obtained from the LAADS (Level 1 and Atmosphere Archive and Distribution System) Web site, where the 
location of the site and the required period is provided as input. The daily AOT data are available for retrieval but the supplied images are given 
in geodetic coordinates.


\subsection{Geographic re-projection}

The necessary transformation from geodetic to geographic coordinates was done using a re-projection script and was applied to each image file using the 
program HDFLook. The re-projected images were constructed with a resolution of 10~km $\times$ 10~km per pixel, which is the maximum possible resolution 
of the system. In this way, the site location can be obtained at the pixel position of the selected site.


\subsection{Data extraction of AOT\\ (470, 550, 660 y 2130 nm)}

Using the re-projected images the final data extraction of the aerosol optical thickness, AOT, was done with another script, using the HDFLook program.


\subsection{Temporal AOT  for SPM}

The data were extracted year by year to avoid errors. For the period 2000--2008 the total number of registers found was 1078, with a different number 
of measurements found at each wavelength.


%%%%%% FIGURA 1

\begin{figure*}[!t]
\centerline{\includegraphics[clip,height=5.22cm,width=0.85\textwidth]{maraizafig1aBN.eps}}
\centerline{\includegraphics[clip,height=5.22cm,width=0.85\textwidth]{maraizafig1bBN.eps}}
\centerline{\includegraphics[clip,height=5.22cm,width=0.85\textwidth]{maraizafig1cBN.eps}}
\centerline{\includegraphics[clip,height=5.22cm,width=0.85\textwidth]{maraizafig1dBN.eps}}
\caption{The average seasonal (March to May for spring, June to August for summer, September to 
November for autumn, and December to February for winter) AOT above SPM over the years 2000--2008.
The color figure can be viewed online.}
\label{fig:figura1}
\end{figure*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5


%%%%% TABLA 3

\begin{table*}[!t]
\vspace{0.1cm}
\centering
\tablecols{10}
\caption{Mean seasonal variation of AOT yearly measurements for 2000--2008} 
\label{tab:seasonal}
\scriptsize
\begin{tabular}{cccccccccc}
\toprule
   & \multicolumn{4}{c}{Number of AOT Measurements} &  & \multicolumn{4}{c}{Seasonal AOT Measurement} \\ 
\cmidrule{2-5} 
\cmidrule{7-10}
Year & 470~nm & 550~nm & 660~nm & 2130~nm &  & 470~nm & 550~nm & 660~nm & 2130~nm \\
\cmidrule{1-10}
\multicolumn{10}{c}{SPRING} \\
\cmidrule{1-10}
00   & 61 & 61 & 61 & 60 & & 0.180 $\pm$ 0.089 & 0.156 $\pm$ 0.076 & 0.138 $\pm$ 0.068 & 0.101 $\pm$ 0.058\\
01   & 43 & 43 & 43 & 43 & & 0.212 $\pm$ 0.084 & 0.183 $\pm$ 0.072 & 0.162 $\pm$ 0.065 & 0.116 $\pm$ 0.061\\
02   & 52 & 52 & 52 & 52 & & 0.172 $\pm$ 0.097 & 0.149 $\pm$ 0.084 & 0.133 $\pm$ 0.075 & 0.097 $\pm$ 0.063\\
03   & 52 & 52 & 52 & 51 & & 0.217 $\pm$ 0.134 & 0.188 $\pm$ 0.116 & 0.168 $\pm$ 0.105 & 0.124 $\pm$ 0.089\\
04   & 53 & 53 & 53 & 51 & & 0.151 $\pm$ 0.094 & 0.132 $\pm$ 0.080 & 0.118 $\pm$ 0.071 & 0.090 $\pm$ 0.056\\
05   & 44 & 44 & 44 & 44 & & 0.181 $\pm$ 0.121 & 0.161 $\pm$ 0.108 & 0.146 $\pm$ 0.099 & 0.115 $\pm$ 0.081\\
06   & 33 & 33 & 33 & 33 & & 0.138 $\pm$ 0.083 & 0.123 $\pm$ 0.074 & 0.113 $\pm$ 0.068 & 0.089 $\pm$ 0.054\\
07   & 43 & 43 & 43 & 41 & & 0.163 $\pm$ 0.089 & 0.144 $\pm$ 0.077 & 0.130 $\pm$ 0.070 & 0.104 $\pm$ 0.054\\
08   & 42 & 42 & 43 & 43 & & 0.144 $\pm$ 0.083 & 0.125 $\pm$ 0.070 & 0.111 $\pm$ 0.060 & 0.081 $\pm$ 0.045\\ 
\cmidrule{1-10}
{\bf 2000--2008} & 423 & 423 & 424 & 418 &  & 0.173 $\pm$0.026 &  0.151 $\pm$ 0.022 & 0.135 $\pm$ 0.019 & 0.102 $\pm$ 0.014 \\
\cmidrule{1-10}
\multicolumn{10}{c}{SUMMER} \\
\cmidrule{1-10}
00   & 29 & 29 & 29 & 29 & & 0.160 $\pm$ 0.090 & 0.141 $\pm$ 0.080 & 0.127 $\pm$ 0.073 & 0.096 $\pm$ 0.061\\
01   & 33 & 33 & 33 & 33 & & 0.126 $\pm$ 0.093 & 0.112 $\pm$ 0.083 & 0.101 $\pm$ 0.075 & 0.078 $\pm$ 0.061\\
02   & 49 & 49 & 50 & 50 & & 0.224 $\pm$ 0.170 & 0.197 $\pm$ 0.154 & 0.178 $\pm$ 0.142 & 0.134 $\pm$ 0.122\\
03   & 30 & 30 & 30 & 30 & & 0.181 $\pm$ 0.086 & 0.159 $\pm$ 0.078 & 0.143 $\pm$ 0.074 & 0.107 $\pm$ 0.066\\
04   & 44 & 44 & 44 & 43 & & 0.144 $\pm$ 0.100 & 0.124 $\pm$ 0.083 & 0.109 $\pm$ 0.072 & 0.079 $\pm$ 0.056\\
05   & 31 & 31 & 31 & 30 & & 0.139 $\pm$ 0.094 & 0.124 $\pm$ 0.083 & 0.113 $\pm$ 0.075 & 0.091 $\pm$ 0.059\\
06   & 29 & 29 & 29 & 29 & & 0.122 $\pm$ 0.077 & 0.105 $\pm$ 0.064 & 0.092 $\pm$ 0.055 & 0.065 $\pm$ 0.043\\
07   & 34 & 34 & 36 & 36 & & 0.185 $\pm$ 0.092 & 0.160 $\pm$ 0.080 & 0.143 $\pm$ 0.071 & 0.102 $\pm$ 0.064\\
08   & 34 & 34 & 34 & 34 & & 0.136 $\pm$ 0.096 & 0.120 $\pm$ 0.084 & 0.109 $\pm$ 0.076 & 0.084 $\pm$ 0.060\\ 
\cmidrule{1-10}
{\bf 2000--2008} & 313 & 313 & 316 & 314 &  & 0.157 $\pm$ 0.032 &  0.138 $\pm$ 0.028 & 0.124 $\pm$ 0.025 & 0.093 $\pm$ 0.019 \\
\cmidrule{1-10}
\multicolumn{10}{c}{AUTUMN} \\
\cmidrule{1-10}
00 & 22 & 22 & 22 & 22 & & 0.101 $\pm$ 0.066 & 0.087 $\pm$ 0.053 & 0.077 $\pm$ 0.046 & 0.055 $\pm$ 0.034\\
01 & 27 & 27 & 27 & 27 & & 0.105 $\pm$ 0.062 & 0.093 $\pm$ 0.056 & 0.084 $\pm$ 0.052 & 0.064 $\pm$ 0.043\\
02 & 30 & 30 & 31 & 30 & & 0.089 $\pm$ 0.058 & 0.080 $\pm$ 0.051 & 0.073 $\pm$ 0.046 & 0.060 $\pm$ 0.034\\
03 & 29 & 28 & 31 & 30 & & 0.085 $\pm$ 0.079 & 0.078 $\pm$ 0.067 & 0.078 $\pm$ 0.063 & 0.062 $\pm$ 0.048\\
04 & 23 & 23 & 23 & 23 & & 0.084 $\pm$ 0.052 & 0.074 $\pm$ 0.046 & 0.067 $\pm$ 0.042 & 0.052 $\pm$ 0.034\\
05 & 38 & 38 & 39 & 38 & & 0.059 $\pm$ 0.062 & 0.052 $\pm$ 0.054 & 0.048 $\pm$ 0.048 & 0.037 $\pm$ 0.037\\
06 & 25 & 25 & 27 & 27 & & 0.082 $\pm$ 0.056 & 0.072 $\pm$ 0.050 & 0.067 $\pm$ 0.045 & 0.052 $\pm$ 0.036\\
07 & 25 & 25 & 27 & 26 & & 0.093 $\pm$ 0.068 & 0.081 $\pm$ 0.058 & 0.074 $\pm$ 0.049 & 0.056 $\pm$ 0.037\\
08 & 30 & 30 & 33 & 32 & & 0.099 $\pm$ 0.071 & 0.088 $\pm$ 0.063 & 0.083 $\pm$ 0.055 & 0.067 $\pm$ 0.043\\
\cmidrule{1-10}
{\bf 2000--2008} & 249 & 248 & 260 & 255 &  & 0.089 $\pm$ 0.013 &  0.078 $\pm$ 0.011 & 0.072 $\pm$ 0.010 & 0.056 $\pm$ 0.008 \\
\cmidrule{1-10}
\multicolumn{10}{c}{WINTER} \\
\cmidrule{1-10}
00-01 & ~2 & ~2 & ~2 & ~2 & & 0.084 $\pm$ 0.141 & 0.076 $\pm$ 0.124 & 0.070 $\pm$ 0.112 & 0.058 $\pm$ 0.085\\
01-02 & 10 & 10 & 12 & 11 & & 0.111 $\pm$ 0.074 & 0.096 $\pm$ 0.063 & 0.085 $\pm$ 0.050 & 0.068 $\pm$ 0.037\\
02-03 & ~8 & ~8 & ~9 & ~9 & & 0.205 $\pm$ 0.164 & 0.183 $\pm$ 0.149 & 0.158 $\pm$ 0.132 & 0.124 $\pm$ 0.110\\
03-04 & 12 & 12 & 13 & 13 & & 0.142 $\pm$ 0.099 & 0.126 $\pm$ 0.089 & 0.113 $\pm$ 0.078 & 0.089 $\pm$ 0.063\\
04-05 & ~2 & ~2 & ~2 & ~2 & & 0.096 $\pm$ 0.018 & 0.070 $\pm$ 0.013 & 0.053 $\pm$ 0.010 & 0.013 $\pm$ 0.002\\
05-06 & 11 & 11 & 11 & 11 & & 0.041 $\pm$ 0.040 & 0.036 $\pm$ 0.036 & 0.033 $\pm$ 0.033 & 0.024 $\pm$ 0.027\\
06-07 & 13 & 13 & 14 & 14 & & 0.135 $\pm$ 0.095 & 0.118 $\pm$ 0.082 & 0.103 $\pm$ 0.072 & 0.074 $\pm$ 0.061 \\
07-08 & ~5 & ~5 & ~6 & ~6 & & 0.147 $\pm$ 0.047 & 0.129 $\pm$ 0.046 & 0.114 $\pm$ 0.041 & 0.086 $\pm$ 0.040 \\
\cmidrule{1-10}
{\bf 2000--2008} & 63 & 63 & 69 & 68 && 0.120 $\pm$ 0.046 &  0.104 $\pm$ 0.042 & 0.091 $\pm$ 0.037 & 0.067 $\pm$ 0.033 \\
\bottomrule
\end{tabular}
\vspace{0.4cm}
\end{table*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\section{Results}

The aerosol optical thickness for the SPM site was obtained and analyzed at the four wavelengths 4700, 5500, 6600 y 21300~\AA. We explore the seasonal, 
monthly and annual behavior of the AOT in the 2000 to 2008 period.


\subsection{Seasonal AOT at SPM}

To study the seasonal variations of the AOT, we use the common season definition for a Northern Hemisphere location, i.e. March to May for spring, 
June to August for summer, September to November for autumn, and December to February for winter. 

In the four panels of Figure~\ref{fig:figura1} we show the seasonal behavior of the AOT at the central wavelengths 4700, 5500, 6600 and 21300~\AA. 
All the plots show that AOT values decrease with wavelength, as expected, and that the same variations are observed at each wavelength. In all the 
curves we note that the AOT is quite small, less than 0.25 for all wavelengths. In some years AOT values even less than 0.10 were obtained, specially 
during autumn. 

In Table~\ref{tab:seasonal} we present the characteristics of the AOT seasonal measurements for each year during the  period covered, 2000--2008, 
together with the resulting AOT mean values for each season and the standard deviation obtained at the four wavelengths.

By comparing the AOT values presented in Table~\ref{tab:seasonal} for the four seasons, we note that the lowest values are obtained in the autumn and 
winter months, being highest during the spring months. This is clearly seen in Figure~\ref{fig:seasonal} which shows the average seasonal AOT behavior 
with wavelength (cf. Table~\ref{tab:seasonal}). The lowest aerosol optical thickness values occur during the autumn months with average values of 
$0.089 \pm 0.013$ at 4700~\AA,  $0.078 \pm 0.011$ at 5500~\AA, $0.072 \pm 0.010$ at 6600~\AA, and $0.056 \pm 0.008$ at 21300~\AA. This allows us to 
conclude that in autumn the atmospheric transparency due to aerosols is best at SPM. 


%%%%% FIGURA 2

\begin{figure}[!t]
\vspace{0.15cm}
\centering
\includegraphics[clip,width=0.99\columnwidth]{maraizafig2BN.eps}
\caption{The average seasonal aerosol optical depth spectral. Error bars show the 
estimated errors of the mean. The lowest aerosol optical thickness values occur 
during the autumn months.}
\label{fig:seasonal}
\vspace{0.5cm}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\subsection{Monthly AOT at SPM}

In Figure~\ref{fig:figura2} we show the monthly behavior of the AOT at four wavelengths 470, 550, 660 and 2130~nm for the 2000 to 2008 period. 
For best comparison the AOT scale in all the graphs is the same. We note that in some years the months of January, February and December show 
scarce or no available data, while in March 2006 we found no data.  The months of April to November were well covered throughout the 2000--2008 
period and so the average values are more robust.  

By comparing the AOT values in the twelve months we note that the lowest values are obtained in October and November, with mean values of less than 
0.12 for all wavelengths. At 550~nm, which is close to the Johnson $V$-band, the average values in October and November are $0.074 \pm 0.013$ and 
$0.068 \pm 0.021$, respectively. We conclude that at all wavelengths October and November are the months with higher atmospheric transparency. 

In Table~\ref{tab:monthly} we present the characteristics of the AOT monthly measurements during the period 2000--2008, together with the resulting 
AOT average values and standard deviation.

Atmospheric extinction measurements at San Pedro M\'artir have been reported by Schuster, Parrao, \& Guichard (2002), and  Schuster \& Parrao 
(2001) for the years 1973--1999, and are summarized in Parrao \& Schuster (2003). Individual nightly determinations of the atmospheric extinction 
above SPM are presented for 82 nights of 13-color photometric observations over the years 1980--1983 and from 287 nights of {\it ubvy} observations 
over the years 1984--1999. Monthly and yearly averages are given and compared for the years 1973--1999 in Schuster et al. (2002). Monthly data of 
atmospheric extinction above SPM covering the full period 2000--2008 are not available and so we can only compare our monthly AOT with the 
1973--1999 of Schuster and collaborators. Their Tables~4, 5, and 6 show monthly averages that can be compared with our AOT mean values for the years 
2000--2008.
 
Schuster et al. (2002) conclude that the best months for photometric observations at SPM are October and November when the atmospheric extinction 
is quite low, $<$$\kappa_y$$>~\sim 0.1223 \pm 0.0022$ \,for October and $0.1195 \pm 0.0022$ for November, and that also during these months the 
observing runs are mostly stable. From their 13-color photometry they conclude that during the September, October and November months the mean 
observed atmospheric extinction at 5827~\AA\ reaches the lowest values $0.1042 \pm 0.0021$, $0.1155 \pm 0.0022$ and $0.1128 \pm 0.0028$, respectively. 
These results for atmospheric extinction agree with our results for the aerosol optical depth over SPM:  indeed October and November are the months 
with higher atmospheric transparency. 


%%%%%% FIGURA 3

\begin{figure*}[!t]
\centerline{\includegraphics[clip,height=3.58cm,width=0.99\columnwidth]{maraizafig3aBN.eps}%
\hspace{\columnsep}%
\includegraphics[clip,height=3.58cm,width=0.99\columnwidth]{maraizafig3bBN.eps}}
\centerline{\includegraphics[clip,height=3.58cm,width=0.99\columnwidth]{maraizafig3cBN.eps}%
\hspace{\columnsep}%
\includegraphics[clip,height=3.58cm,width=0.99\columnwidth]{maraizafig3dBN.eps}}
\centerline{\includegraphics[clip,height=3.58cm,width=0.99\columnwidth]{maraizafig3eBN.eps}%
\hspace{\columnsep}%
\includegraphics[clip,height=3.58cm,width=0.99\columnwidth]{maraizafig3fBN.eps}}
\centerline{\includegraphics[clip,height=3.58cm,width=0.99\columnwidth]{maraizafig3gBN.eps}%
\hspace{\columnsep}%
\includegraphics[clip,height=3.58cm,width=0.99\columnwidth]{maraizafig3hBN.eps}}
\centerline{\includegraphics[clip,height=3.58cm,width=0.99\columnwidth]{maraizafig3iBN.eps}%
\hspace{\columnsep}%
\includegraphics[clip,height=3.58cm,width=0.99\columnwidth]{maraizafig3jBN.eps}}
\centerline{\includegraphics[clip,height=3.58cm,width=0.99\columnwidth]{maraizafig3kBN.eps}%
\hspace{\columnsep}%
\includegraphics[clip,height=3.58cm,width=0.99\columnwidth]{maraizafig3lBN.eps}}
\caption{Monthly Average (January to December) 2000--2008. The color figure can be viewed online.}
\label{fig:figura2}
\end{figure*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%% TABLA 4


\begin{table*}[!t]
\vspace{0.1cm}
\centering
\tablecols{10}
\caption{Average Monthly AOT above SPM over the years 2000--2008}
\label{tab:monthly}
\scriptsize
\begin{tabular}{cccccccccc}
\toprule
   & \multicolumn{4}{c}{Number of AOT Measurements} &  & \multicolumn{4}{c}{Monthly AOT Measurement} \\ 
\cmidrule{2-5} 
\cmidrule{7-10}
Year & 470~nm & 550~nm & 660~nm & 2130~nm &  & 470~nm & 550~nm & 660~nm & 2130~nm \\
\cmidrule{1-10}
\multicolumn{10}{c}{JANUARY} \\
\cmidrule{1-10}
02 & 3 & 3 & 4 & 4 && 0.095 $\pm$ 0.032 & 0.084 $\pm$ 0.029 & 0.083 $\pm$ 0.024 & 0.066 $\pm$ 0.019\\
03 & 4 & 4 & 5 & 5 && 0.111 $\pm$ 0.059 & 0.097 $\pm$ 0.055 & 0.087 $\pm$ 0.046 & 0.065 $\pm$ 0.041\\
04 & 3 & 3 & 4 & 4 && 0.062 $\pm$ 0.083 & 0.053 $\pm$ 0.073 & 0.058 $\pm$ 0.058 & 0.043 $\pm$ 0.047\\
06 & 6 & 6 & 6 & 6 && 0.048 $\pm$ 0.039 & 0.041 $\pm$ 0.036 & 0.036 $\pm$ 0.034 & 0.024 $\pm$ 0.030\\
07 & 1 & 1 & 1 & 1 && 0.099 $\pm$ \nodata~~~ & 0.089 $\pm$ \nodata~~~ & 0.081 $\pm$ \nodata~~~ & 0.064 $\pm$ \nodata~~~~\\
08 & 0 & 0 & 1 & 1 && \nodata ~$\pm$ \nodata & \nodata ~~$\pm$ \nodata~ & 0.111 $\pm$ \nodata~~~ & 0.088 $\pm$ \nodata~~~~\\
\cmidrule{1-10}
\multicolumn{10}{c}{FEBRUARY} \\
\cmidrule{1-10}
00 & 2 & 2 & 2 & 2 && 0.115 $\pm$ 0.063 & 0.103 $\pm$ 0.056 & 0.093 $\pm$ 0.051 & 0.074 $\pm$ 0.040\\
02 & 5 & 5 & 6 & 6 && 0.140 $\pm$ 0.085 & 0.119 $\pm$ 0.072 & 0.098 $\pm$ 0.059 & 0.068 $\pm$ 0.050\\
03 & 2 & 2 & 2 & 2 && 0.286 $\pm$ 0.051 & 0.256 $\pm$ 0.046 & 0.234 $\pm$ 0.042 & 0.186 $\pm$ 0.035\\
05 & 1 & 1 & 1 & 1 && 0.083 $\pm$ \nodata~~~ & 0.061 $\pm$ \nodata~~~ & 0.046 $\pm$ \nodata~~~ & 0.011 $\pm$ \nodata~~~~\\
06 & 3 & 3 & 3 & 3 && 0.035 $\pm$ 0.028 & 0.031 $\pm$ 0.025 & 0.028 $\pm$ 0.023 & 0.022 $\pm$ 0.018\\
07 & 1 & 1 & 2 & 2 && 0.117 $\pm$ \nodata~~~ & 0.105 $\pm$ \nodata~~~ & 0.080 $\pm$ 0.021 & 0.046 $\pm$ 0.043\\
08 & 2 & 2 & 2 & 2 && 0.173 $\pm$ 0.045 & 0.155 $\pm$ 0.040 & 0.141 $\pm$ 0.037 & 0.112 $\pm$ 0.029\\
\cmidrule{1-10}
\multicolumn{10}{c}{MARCH} \\
\cmidrule{1-10}
00 & ~9 & ~9 & ~9 & ~9 && 0.135 $\pm$ 0.072 & 0.113 $\pm$ 0.057 & 0.097 $\pm$ 0.049 & 0.062 $\pm$ 0.044\\
01 & ~3 & ~3 & ~3 & ~3 && 0.232 $\pm$ 0.092 & 0.192 $\pm$ 0.070 & 0.163 $\pm$ 0.060 & 0.099 $\pm$ 0.071\\
02 & ~5 & ~5 & ~5 & ~4 && 0.123 $\pm$ 0.083 & 0.103 $\pm$ 0.064 & 0.089 $\pm$ 0.052 & 0.071 $\pm$ 0.028\\
03 & ~8 & ~8 & ~8 & ~8 && 0.169 $\pm$ 0.185 & 0.152 $\pm$ 0.166 & 0.140 $\pm$ 0.152 & 0.114 $\pm$ 0.123\\
04 & 14 & 14 & 14 & 14 && 0.135 $\pm$ 0.089 & 0.121 $\pm$ 0.080 & 0.110 $\pm$ 0.073 & 0.087 $\pm$ 0.058\\
05 & ~2 & ~2 & ~2 & ~2 && 0.075 $\pm$ 0.047 & 0.058 $\pm$ 0.030 & 0.047 $\pm$ 0.019 & 0.020 $\pm$ 0.008\\
07 & 13 & 13 & 13 & 12 && 0.133 $\pm$ 0.103 & 0.116 $\pm$ 0.090 & 0.104 $\pm$ 0.081 & 0.084 $\pm$ 0.065\\
08 & ~8 & ~8 & ~8 & ~8 && 0.122 $\pm$ 0.047 & 0.104 $\pm$ 0.043 & 0.091 $\pm$ 0.041 & 0.062 $\pm$ 0.041\\
\cmidrule{1-10}
\multicolumn{10}{c}{APRIL} \\
\cmidrule{1-10}
00 & 19 & 19 & 19 & 18 && 0.169 $\pm$ 0.086 & 0.146 $\pm$ 0.073 & 0.129 $\pm$ 0.065 & 0.096 $\pm$ 0.054\\
01 & 14 & 14 & 14 & 14 && 0.222 $\pm$ 0.068 & 0.188 $\pm$ 0.059 & 0.164 $\pm$ 0.056 & 0.110 $\pm$ 0.063\\
02 & 15 & 15 & 15 & 15 && 0.142 $\pm$ 0.090 & 0.127 $\pm$ 0.081 & 0.116 $\pm$ 0.073 & 0.092 $\pm$ 0.058\\
03 & 11 & 11 & 11 & 10 && 0.173 $\pm$ 0.131 & 0.150 $\pm$ 0.111 & 0.133 $\pm$ 0.098 & 0.106 $\pm$ 0.075\\
04 & 11 & 11 & 11 & 11 && 0.155 $\pm$ 0.073 & 0.135 $\pm$ 0.066 & 0.120 $\pm$ 0.062 & 0.086 $\pm$ 0.058\\
05 & 19 & 19 & 19 & 19 && 0.179 $\pm$ 0.137 & 0.157 $\pm$ 0.121 & 0.142 $\pm$ 0.111 & 0.109 $\pm$ 0.092\\
06 & 12 & 12 & 12 & 12 && 0.135 $\pm$ 0.079 & 0.121 $\pm$ 0.070 & 0.111 $\pm$ 0.063 & 0.089 $\pm$ 0.048\\
07 & 14 & 14 & 14 & 14 && 0.160 $\pm$ 0.092 & 0.140 $\pm$ 0.076 & 0.125 $\pm$ 0.067 & 0.092 $\pm$ 0.054\\
08 & 11 & 11 & 12 & 12 && 0.151 $\pm$ 0.049 & 0.131 $\pm$ 0.046 & 0.116 $\pm$ 0.042 & 0.085 $\pm$ 0.043\\
\cmidrule{1-10}
\multicolumn{10}{c}{MAY} \\
\cmidrule{1-10}
00 & 22 & 22 & 22 & 22 && 0.176 $\pm$ 0.081 & 0.151 $\pm$ 0.066 & 0.133 $\pm$ 0.058 & 0.093 $\pm$ 0.053\\
01 & 16 & 16 & 16 & 16 && 0.225 $\pm$ 0.101 & 0.196 $\pm$ 0.087 & 0.175 $\pm$ 0.078 & 0.130 $\pm$ 0.069\\
02 & 18 & 18 & 18 & 18 && 0.169 $\pm$ 0.108 & 0.147 $\pm$ 0.092 & 0.131 $\pm$ 0.081 & 0.095 $\pm$ 0.065\\
03 & 20 & 20 & 20 & 20 && 0.258 $\pm$ 0.138 & 0.224 $\pm$ 0.123 & 0.200 $\pm$ 0.113 & 0.147 $\pm$ 0.102\\
04 & 23 & 23 & 23 & 22 && 0.167 $\pm$ 0.099 & 0.145 $\pm$ 0.084 & 0.130 $\pm$ 0.074 & 0.100 $\pm$ 0.057\\
05 & 18 & 18 & 18 & 18 && 0.201 $\pm$ 0.115 & 0.180 $\pm$ 0.103 & 0.165 $\pm$ 0.095 & 0.132 $\pm$ 0.077\\
06 & 10 & 10 & 10 & 10 && 0.150 $\pm$ 0.085 & 0.132 $\pm$ 0.078 & 0.119 $\pm$ 0.073 & 0.091 $\pm$ 0.064\\
07 & 14 & 14 & 14 & 13 && 0.181 $\pm$ 0.093 & 0.160 $\pm$ 0.083 & 0.144 $\pm$ 0.077 & 0.120 $\pm$ 0.059\\
08 & 13 & 13 & 13 & 13 && 0.145 $\pm$ 0.081 & 0.128 $\pm$ 0.071 & 0.116 $\pm$ 0.064 & 0.090 $\pm$ 0.049\\
\cmidrule{1-10}
\multicolumn{10}{c}{JUNE} \\
\cmidrule{1-10}
00 & 18 & 18 & 18 & 18 && 0.196 $\pm$ 0.102 & 0.174 $\pm$ 0.090 & 0.157 $\pm$ 0.082 & 0.122 $\pm$ 0.066\\
01 & 10 & 10 & 10 & 10 && 0.173 $\pm$ 0.071 & 0.153 $\pm$ 0.063 & 0.139 $\pm$ 0.057 & 0.109 $\pm$ 0.044\\
02 & 23 & 23 & 23 & 23 && 0.212 $\pm$ 0.119 & 0.185 $\pm$ 0.106 & 0.166 $\pm$ 0.099 & 0.123 $\pm$ 0.087\\
03 & 21 & 21 & 21 & 21 && 0.225 $\pm$ 0.108 & 0.195 $\pm$ 0.092 & 0.173 $\pm$ 0.083 & 0.124 $\pm$ 0.073\\
04 & 20 & 20 & 20 & 19 && 0.145 $\pm$ 0.100 & 0.127 $\pm$ 0.085 & 0.115 $\pm$ 0.075 & 0.091 $\pm$ 0.056\\
05 & 10 & 10 & 10 & 10 && 0.139 $\pm$ 0.089 & 0.124 $\pm$ 0.080 & 0.113 $\pm$ 0.073 & 0.090 $\pm$ 0.058\\
06 & 11 & 11 & 11 & 11 && 0.132 $\pm$ 0.093 & 0.118 $\pm$ 0.082 & 0.108 $\pm$ 0.073 & 0.087 $\pm$ 0.056\\
07 & 15 & 15 & 15 & 15 && 0.148 $\pm$ 0.082 & 0.132 $\pm$ 0.073 & 0.120 $\pm$ 0.067 & 0.096 $\pm$ 0.054\\
08 & 19 & 19 & 19 & 19 && 0.141 $\pm$ 0.104 & 0.122 $\pm$ 0.084 & 0.108 $\pm$ 0.070 & 0.078 $\pm$ 0.045\\
\bottomrule
\end{tabular}
\vspace{0.3cm}
\end{table*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%% TABLA 4 CONTINUA

\setcounter{table}{3}
\begin{table*}[!t]
\vspace{0.1cm}
\centering
\centerline{TABLE~4 (CONTINUED)\smallskip}
\tablecols{10}
\scriptsize
\begin{tabular}{cccccccccc}
\toprule
   & \multicolumn{4}{c}{Number of AOT Measurements} &  & \multicolumn{4}{c}{Monthly AOT Measurement} \\ 
\cmidrule{2-5} 
\cmidrule{7-10}
Year & 470~nm & 550~nm & 660~nm & 2130~nm &  & 470~nm & 550~nm & 660~nm & 2130~nm \\
\cmidrule{1-10}
\multicolumn{10}{c}{JULY} \\
\cmidrule{1-10}
00 & 12 & 12 & 12 & 12 && 0.186 $\pm$ 0.122 & 0.164 $\pm$ 0.107 & 0.149 $\pm$ 0.097 & 0.114 $\pm$ 0.079\\
01 & 12 & 12 & 12 & 12 && 0.124 $\pm$ 0.066 & 0.109 $\pm$ 0.056 & 0.099 $\pm$ 0.049 & 0.076 $\pm$ 0.038\\
02 & 16 & 16 & 16 & 16 && 0.215 $\pm$ 0.105 & 0.187 $\pm$ 0.094 & 0.167 $\pm$ 0.087 & 0.124 $\pm$ 0.078\\
03 & ~6 & ~6 & ~6 & ~6 && 0.248 $\pm$ 0.118 & 0.222 $\pm$ 0.106 & 0.203 $\pm$ 0.097 & 0.162 $\pm$ 0.078\\
04 & 16 & 16 & 16 & 16 && 0.188 $\pm$ 0.099 & 0.161 $\pm$ 0.083 & 0.142 $\pm$ 0.074 & 0.099 $\pm$ 0.065\\
05 & 13 & 13 & 13 & 12 && 0.164 $\pm$ 0.101 & 0.147 $\pm$ 0.090 & 0.134 $\pm$ 0.083 & 0.116 $\pm$ 0.060\\
06 & ~8 & ~8 & ~8 & ~8 && 0.153 $\pm$ 0.060 & 0.137 $\pm$ 0.054 & 0.125 $\pm$ 0.049 & 0.099 $\pm$ 0.039\\
07 & 13 & 13 & 14 & 14 && 0.221 $\pm$ 0.100 & 0.194 $\pm$ 0.085 & 0.172 $\pm$ 0.073 & 0.129 $\pm$ 0.064\\
08 & 11 & 11 & 11 & 11 && 0.123 $\pm$ 0.110 & 0.109 $\pm$ 0.096 & 0.099 $\pm$ 0.086 & 0.076 $\pm$ 0.065\\
\cmidrule{1-10}
\multicolumn{10}{c}{AUGUST} \\
\cmidrule{1-10}
00 & ~3 & ~3 & ~3 & ~3 && 0.175 $\pm$ 0.067 & 0.147 $\pm$ 0.058 & 0.126 $\pm$ 0.055 & 0.079 $\pm$ 0.062\\
01 & ~9 & ~9 & ~9 & ~9 && 0.150 $\pm$ 0.145 & 0.131 $\pm$ 0.131 & 0.118 $\pm$ 0.121 & 0.088 $\pm$ 0.102\\
02 & 15 & 15 & 16 & 16 && 0.261 $\pm$ 0.248 & 0.229 $\pm$ 0.227 & 0.206 $\pm$ 0.205 & 0.156 $\pm$ 0.179\\
03 & ~8 & ~8 & ~8 & ~8 && 0.184 $\pm$ 0.057 & 0.159 $\pm$ 0.056 & 0.141 $\pm$ 0.056 & 0.101 $\pm$ 0.061\\
04 & 13 & 13 & 13 & 13 && 0.121 $\pm$ 0.114 & 0.101 $\pm$ 0.090 & 0.086 $\pm$ 0.074 & 0.053 $\pm$ 0.051\\
05 & ~6 & ~6 & ~6 & ~6 && 0.150 $\pm$ 0.097 & 0.130 $\pm$ 0.084 & 0.116 $\pm$ 0.075 & 0.084 $\pm$ 0.062\\
06 & 14 & 14 & 14 & 14 && 0.091 $\pm$ 0.075 & 0.079 $\pm$ 0.062 & 0.070 $\pm$ 0.053 & 0.049 $\pm$ 0.039\\
07 & ~9 & ~9 & ~9 & ~9 && 0.190 $\pm$ 0.103 & 0.165 $\pm$ 0.091 & 0.148 $\pm$ 0.083 & 0.109 $\pm$ 0.072\\
08 & 10 & 10 & 10 & 10 && 0.145 $\pm$ 0.100 & 0.130 $\pm$ 0.089 & 0.118 $\pm$ 0.081 & 0.094 $\pm$ 0.065\\
\cmidrule{1-10}
\multicolumn{10}{c}{SEPTEMBER} \\
\cmidrule{1-10}
00 & 18 & 18 & 18 & 18 && 0.131 $\pm$ 0.054 & 0.116 $\pm$ 0.049 & 0.105 $\pm$ 0.046 & 0.081 $\pm$ 0.039\\
01 & 16 & 16 & 16 & 16 && 0.118 $\pm$ 0.067 & 0.106 $\pm$ 0.058 & 0.097 $\pm$ 0.052 & 0.078 $\pm$ 0.040\\
02 & 17 & 17 & 17 & 16 && 0.158 $\pm$ 0.109 & 0.139 $\pm$ 0.095 & 0.125 $\pm$ 0.086 & 0.100 $\pm$ 0.068\\
03 & 14 & 14 & 14 & 14 && 0.129 $\pm$ 0.052 & 0.112 $\pm$ 0.045 & 0.099 $\pm$ 0.041 & 0.071 $\pm$ 0.038\\
04 & 14 & 14 & 14 & 13 && 0.105 $\pm$ 0.068 & 0.093 $\pm$ 0.061 & 0.085 $\pm$ 0.055 & 0.073 $\pm$ 0.041\\
05 & 11 & 11 & 12 & 12 && 0.090 $\pm$ 0.060 & 0.081 $\pm$ 0.052 & 0.077 $\pm$ 0.046 & 0.062 $\pm$ 0.036\\
06 & ~9 & ~9 & ~9 & ~9 && 0.137 $\pm$ 0.075 & 0.114 $\pm$ 0.058 & 0.097 $\pm$ 0.048 & 0.059 $\pm$ 0.037\\
07 & 15 & 15 & 16 & 16 && 0.141 $\pm$ 0.060 & 0.119 $\pm$ 0.048 & 0.106 $\pm$ 0.042 & 0.065 $\pm$ 0.037\\
08 & 11 & 11 & 11 & 11 && 0.158 $\pm$ 0.091 & 0.139 $\pm$ 0.080 & 0.125 $\pm$ 0.072 & 0.094 $\pm$ 0.060\\
\cmidrule{1-10}
\multicolumn{10}{c}{OCTOBER} \\
\cmidrule{1-10}
00 & 10 & 10 & 10 & 10 && 0.104 $\pm$ 0.067 & 0.087 $\pm$ 0.051 & 0.076 $\pm$ 0.041 & 0.050 $\pm$ 0.027\\
01 & 12 & 12 & 12 & 12 && 0.107 $\pm$ 0.060 & 0.093 $\pm$ 0.056 & 0.082 $\pm$ 0.053 & 0.060 $\pm$ 0.047\\
02 & 16 & 16 & 16 & 16 && 0.099 $\pm$ 0.052 & 0.089 $\pm$ 0.046 & 0.081 $\pm$ 0.042 & 0.064 $\pm$ 0.034\\
03 & 15 & 15 & 17 & 16 && 0.074 $\pm$ 0.090 & 0.066 $\pm$ 0.077 & 0.065 $\pm$ 0.065 & 0.054 $\pm$ 0.048\\
04 & 13 & 13 & 13 & 13 && 0.075 $\pm$ 0.047 & 0.065 $\pm$ 0.040 & 0.059 $\pm$ 0.036 & 0.044 $\pm$ 0.029\\
05 & 20 & 20 & 20 & 20 && 0.058 $\pm$ 0.071 & 0.052 $\pm$ 0.060 & 0.047 $\pm$ 0.053 & 0.036 $\pm$ 0.039\\
06 & 13 & 13 & 13 & 13 && 0.093 $\pm$ 0.046 & 0.083 $\pm$ 0.042 & 0.075 $\pm$ 0.039 & 0.058 $\pm$ 0.033\\
07 & 12 & 12 & 14 & 13 && 0.069 $\pm$ 0.065 & 0.061 $\pm$ 0.057 & 0.061 $\pm$ 0.050 & 0.049 $\pm$ 0.039\\
08 & 14 & 14 & 13 & 12 && 0.082 $\pm$ 0.068 & 0.073 $\pm$ 0.061 & 0.072 $\pm$ 0.054 & 0.062 $\pm$ 0.041\\
\cmidrule{1-10}
\multicolumn{10}{c}{NOVEMBER} \\
\cmidrule{1-10}
00 & ~5 & ~5 & ~5 & ~5 && 0.067 $\pm$ 0.088 & 0.057 $\pm$ 0.071 & 0.049 $\pm$ 0.060 & 0.033 $\pm$ 0.040\\
01 & ~9 & ~9 & ~9 & ~9 && 0.092 $\pm$ 0.067 & 0.082 $\pm$ 0.060 & 0.075 $\pm$ 0.054 & 0.060 $\pm$ 0.043\\
02 & ~8 & ~8 & ~9 & ~9 && 0.056 $\pm$ 0.055 & 0.051 $\pm$ 0.047 & 0.048 $\pm$ 0.039 & 0.040 $\pm$ 0.027\\
03 & ~6 & ~5 & ~6 & ~6 && 0.064 $\pm$ 0.076 & 0.065 $\pm$ 0.067 & 0.084 $\pm$ 0.086 & 0.061 $\pm$ 0.071\\
04 & ~5 & ~5 & ~5 & ~5 && 0.087 $\pm$ 0.033 & 0.078 $\pm$ 0.030 & 0.071 $\pm$ 0.027 & 0.056 $\pm$ 0.021\\
05 & 10 & 10 & 10 & ~9 && 0.063 $\pm$ 0.065 & 0.055 $\pm$ 0.058 & 0.050 $\pm$ 0.053 & 0.041 $\pm$ 0.043\\
06 & ~7 & ~7 & ~9 & ~9 && 0.040 $\pm$ 0.040 & 0.036 $\pm$ 0.035 & 0.045 $\pm$ 0.037 & 0.036 $\pm$ 0.028\\
07 & ~6 & ~6 & ~6 & ~6 && 0.123 $\pm$ 0.051 & 0.110 $\pm$ 0.045 & 0.100 $\pm$ 0.042 & 0.079 $\pm$ 0.033\\
08 & 10 & 10 & 13 & 13 && 0.088 $\pm$ 0.047 & 0.078 $\pm$ 0.043 & 0.068 $\pm$ 0.035 & 0.053 $\pm$ 0.030\\
\cmidrule{1-10}
\multicolumn{10}{c}{DECEMBER} \\
\cmidrule{1-10}
00 & 3 & 3 & 3 & 3 && 0.106 $\pm$ 0.107 & 0.095 $\pm$ 0.094 & 0.088 $\pm$ 0.085 & 0.071 $\pm$ 0.064\\
01 & 2 & 2 & 2 & 2 && 0.090 $\pm$ 0.093 & 0.079 $\pm$ 0.081 & 0.071 $\pm$ 0.073 & 0.053 $\pm$ 0.054\\
03 & 4 & 4 & 4 & 4 && 0.110 $\pm$ 0.026 & 0.098 $\pm$ 0.023 & 0.090 $\pm$ 0.021 & 0.071 $\pm$ 0.016\\
05 & 7 & 7 & 7 & 7 && 0.043 $\pm$ 0.046 & 0.037 $\pm$ 0.039 & 0.032 $\pm$ 0.034 & 0.022 $\pm$ 0.025\\
06 & 4 & 4 & 4 & 4 && 0.118 $\pm$ 0.081 & 0.102 $\pm$ 0.074 & 0.092 $\pm$ 0.069 & 0.067 $\pm$ 0.059\\
07 & 1 & 1 & 1 & 1 && 0.041 $\pm$ \nodata~~~ & 0.030 $\pm$ \nodata~~~ & 0.023 $\pm$ \nodata~~~ & 0.005 $\pm$ \nodata~~~~\\
08 & 2 & 2 & 3 & 3 && 0.138 $\pm$ 0.121 & 0.123 $\pm$ 0.109 & 0.121 $\pm$ 0.072 & 0.096 $\pm$ 0.056\\
\bottomrule
\end{tabular}
\end{table*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%% FIGURA 4

\begin{figure*}[!t]
\centering
\includegraphics[clip,width=0.85\textwidth,height=5.295cm]{maraizafig4aBN.eps}
\includegraphics[clip,width=0.85\textwidth,height=5.295cm]{maraizafig4bBN.eps}
\includegraphics[clip,width=0.85\textwidth,height=5.295cm]{maraizafig4cBN.eps}
\includegraphics[clip,width=0.85\textwidth,height=5.295cm]{maraizafig4dBN.eps}
\caption{Annual AOT behavior at the SPM location by monthly average at 470 nm (top), 
550 nm (second from top to bottom), 660 nm (third from top to bottom), and 2130 nm 
(bottom). The color figure can be viewed online.}
\label{fig:figura3}
\end{figure*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5


%%%%% TABLA 5

\setcounter{table}{4}
\begin{table*}[!t]
\vspace{0.1cm}
\centering
\tablecols{11}
\caption{Average Annual AOT above SPM over the years 2000--2008}
\label{tab:anual}
\setlength{\tabcolsep}{0.87\tabcolsep}
\casitiny
\begin{tabular}{ccccccccccc}
\toprule
   &   & \multicolumn{4}{c}{Number of AOT Measurements} &  & \multicolumn{4}{c}{Annual AOT Measurement} \\ 
\cmidrule{3-6} 
\cmidrule{8-11}
Year & Registers & 470~nm & 550~nm & 660~nm & 2130~nm &  & 470~nm & 550~nm & 660~nm & 2130~nm \\
\cmidrule{1-11}
2000 & 121 & 121 & 121 & 121 & 120 && 0.156 $\pm$ 0.089 & 0.135 $\pm$ 0.077 & 0.121 $\pm$ 0.069 & 0.088 $\pm$ 0.057\\
2001 & 103 & 103 & 103 & 103 & 103 && 0.157 $\pm$ 0.094 & 0.137 $\pm$ 0.082 & 0.122 $\pm$ 0.074 & 0.090 $\pm$ 0.061\\
2002 & 145 & 141 & 141 & 145 & 143 && 0.168 $\pm$ 0.131 & 0.147 $\pm$ 0.116 & 0.132 $\pm$ 0.106 & 0.100 $\pm$ 0.088\\
2003 & 123 & 119 & 118 & 122 & 120 && 0.175 $\pm$ 0.124 & 0.154 $\pm$ 0.108 & 0.138 $\pm$ 0.097 & 0.104 $\pm$ 0.080\\
2004 & 133 & 132 & 132 & 133 & 130 && 0.136 $\pm$ 0.093 & 0.119 $\pm$ 0.079 & 0.106 $\pm$ 0.070 & 0.079 $\pm$ 0.055\\
2005 & 118 & 117 & 117 & 118 & 116 && 0.126 $\pm$ 0.109 & 0.112 $\pm$ 0.096 & 0.101 $\pm$ 0.088 & 0.080 $\pm$ 0.071\\
2006 &  99 &  97 &  97 &  99 &  99 && 0.110 $\pm$ 0.076 & 0.097 $\pm$ 0.067 & 0.087 $\pm$ 0.060 & 0.066 $\pm$ 0.048\\
2007 & 119 & 114 & 114 & 119 & 116 && 0.151 $\pm$ 0.092 & 0.132 $\pm$ 0.080 & 0.118 $\pm$ 0.071 & 0.090 $\pm$ 0.058\\
2008 & 117 & 111 & 111 & 116 & 115 && 0.130 $\pm$ 0.084 & 0.114 $\pm$ 0.073 & 0.102 $\pm$ 0.063 & 0.078 $\pm$ 0.049\\
\midrule
Average 2000--2008 & 1078 & 1055 & 1054 & 1076 & 1062 && 0.147 $\pm$ 0.103 & 0.128 $\pm$ 0.090 & 0.115 $\pm$ 0.081 & 0.087 $\pm$ 0.066 \\
\bottomrule
\end{tabular}
\vspace{0.4cm}
\end{table*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%% FIGURA 5

\begin{figure*}[!t]
\centering
\includegraphics[clip,width=0.88\textwidth]{maraizafig5BN.eps}
\caption{Annual aerosol optical depth  average at SPM at 470, 550, 660 and 
2130~nm during the years 2000--2008. The color figure can be viewed online.}
\label{fig:figura4}
\vspace{0.4cm}
\end{figure*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\subsection{Annual behavior of AOT in four wavelengths by monthly average}

In Figure~\ref{fig:figura3} we show the annual behavior of the AOT by monthly average at the four wavelengths 470, 550, 660 and 2130~nm. 
For best comparison the AOT scale in all graphs is kept the same.  By comparing the monthly AOT values we note that lowest values for the 
aerosol optical depth in all wavelength bands are obtained also during October and November in a consistent way through the years 2000--2008. 
As mentioned above, for the months of January and February there are not enough data in the studied period and mean values are less reliable.

In Table~\ref{tab:anual} we present the characteristics of the atmospheric optical depth annual measurements during the years 2000--2008 for 
the SPM location, together with the resulting AOT average values and standard deviation.


\subsection{Annual and general behavior of AOT}

The annual average and the general behavior of the aerosol optical depth for the SPM location for the period 2000--2008 at the four studied 
wavelengths 470, 550, 660 and 2130~nm is shown in Figure~\ref{fig:figura4}.


\subsection{AOT Climatology (2000 -- 2008)}

We conclude that MODIS data obtained during the 2000--2008 of the San Pedro M\'artir astronomical site in Baja California, Mexico yield an AOT 
climatology with the values presented in Table~\ref{tab:climatology}.


%%%%% TABLA 6

\setcounter{table}{5}
\begin{table}[!t]
\vspace{0.1cm}
\centering
\caption{San Pedro M\'artir, Baja California (Mexico) Aerosol Optical Depth climatology 
from MODIS for 2000--2008}
\label{tab:climatology}
\begin{tabular}{ccc}
\toprule
Wavelength & Number of AOT & AOT \\
(nm)       & Measurements  & 2000-2008 \\
\midrule
470  & 1055 & 0.147 $\pm$ 0.103 \\
550  & 1054 & 0.128 $\pm$ 0.090 \\
660  & 1076 & 0.115 $\pm$ 0.081 \\
2130 & 1062 & 0.087 $\pm$ 0.066 \\ 
\bottomrule
\end{tabular}
\vspace{0.5cm}
\end{table}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


The final results could be compared with other sites in the globe. Gupta et al. (2006) presented AOT results for a collection  of 26 locations 
in Sidney, Delhi, Hong Kong, New York City and Switzerland that cover urban populated to rural areas. The results of the rural areas in Australia 
and Switzerland compare quite well with the SPM results; at 550~nm they show mean annual values of $0.10 \pm 0.08$ and $0.16 \pm 0.10$, respectively, 
compared to our results that range from 0.10 to 0.15 in the period studied. On the other hand, Varela et al. (2008) show that in the Canarian 
Observatories site the AOT values found have a much wider range than the SPM values, with some dusty periods that produce a collection of MODIS 
AOT values at 550~nm above 0.40. But they show that, at this observatory site, most of the time the AOT have values between 0.02 and 0.20 (see 
Figures~12 and 13 in Varela et al. 2008). From their data in Figures~12 and 13 their average value is probably $\sim$0.15, reaching values as 
large as $\sim$0.7, but no average values are estimated in their work.


%%%%%% TABLA 7

\setcounter{table}{6}
\begin{table}[!t]
\vspace{0.1cm}
\centering
\caption{Wavelength Dependence of Seasonal Aerosol Opacity over SPM from MODIS for 2000--2008}
\label{tab:spectral}
\begin{tabular}{ccc}
\toprule
Season  & $\alpha_\mathrm{OIR}$ & $\alpha_\mathrm{OP}$  \\
\midrule
spring  & 0.31 $\pm$ 0.06      & 0.73 $\pm$ 0.07 \\
summer  & 0.31 $\pm$ 0.06      & 0.69 $\pm$ 0.07 \\
autumn  & 0.27 $\pm$ 0.05      & 0.62 $\pm$ 0.11 \\
winter  & 0.35 $\pm$ 0.07      & 0.81 $\pm$ 0.05 \\ 
\midrule
Average 2000--2008 & 0.31 $\pm$ 0.06 & 0.72 $\pm$ 0.08 \\
\bottomrule
\end{tabular}
\vspace{0.4cm}
\end{table}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\subsection{AOT Spectral Slopes}

In Table~\ref{tab:spectral} we present linear regression fits to the seasonal AOT values assuming that aerosols have a power-law behavior with 
wavelength of the form 
\begin{equation}
AOT\equiv\tau_A (\lambda) \propto \lambda^{-\alpha}\,.
\end{equation}

As is shown by Junge (1963) if the aerosol refractive indices are constant,  aerosol particles with power-law size distributions given by 
$d N(r) \propto r{-(\beta+1)}$ produce wavelength-dependent  optical depths of the form
\begin{equation}
\tau \, \propto\ \, \lambda^{-(\beta-2)}\,.
\end{equation}
So the slope $\alpha$ above corresponds to the slope $\beta-2$ of these models.


%%%%% FIGURA 6

\begin{figure}[!t]
\vspace{0.15cm}
\centering
\includegraphics[clip,width=0.99\columnwidth]{maraizafig6BN.eps}
\caption{Spectral dependence of aerosol optical depth obtained from MODIS data for 
San Pedro M\'artir. Seasonal data are shown as follows: spring (circle), summer 
(triangle), autumn (square) and winter (plus), together with mean values for the 
2000--2008 period (diamond). The dotted lines represent the linear regression fits 
to the data (c.f. slope values in Table~\ref{tab:spectral}). The color figure can 
be viewed online.}
\label{fig:spectral}
\vspace{0.4cm}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


We have calculated $\alpha$ values, assuming $\tau_\lambda \propto \lambda^\alpha$, for the wavelengths 4700, 5500, 6600 and 21300~\AA\ which are 
labeled OIR (optical to near-infrared) and for the visible region 4700, 5500 and 6600~\AA\ labeled OP, with linear fits to the average seasonal 
AOT values presented in Tables~\ref{tab:seasonal} and \ref{tab:climatology}. The results are presented in Table~\ref{tab:spectral} and graphically 
in Figure~\ref{fig:spectral}. Note that $\alpha_\mathrm{OIR}$ has values between 0.27 (autumn) and 0.35 (winter) while $\alpha_\mathrm{OP}$ has 
values from 0.62 (autumn) to 0.82 (winter). We conclude that for periods with higher atmospheric transparency the spectral slope $\alpha$ is
 smaller and steepens for periods with higher opacity.

We have also used the average values for the years 2000--2008 (c.f. Table~\ref{tab:climatology}) which yield $\alpha_\mathrm{OIR} \sim 0.31 \pm 0.06$ 
($\tau_\lambda \sim 0.0061 \lambda^{-0.31}$) and $\alpha_\mathrm{OP} \sim 0.72 \pm 0.08$ ($\tau_\lambda \sim 0.0001 \lambda^{-0.72}$) for the San Pedro 
M\'artir location.

We can compare these $\alpha$ values with the radiative transfer models of global atmospheric aerosols of Toon \& Pollack (1976). In particular, 
with their Figure~8b where the contribution of different layers of the atmosphere is shown to produce a steepening in their calculated optical 
depth $\tau(\lambda)$ curves in the 0.1 to 10~$\mu$m interval, with values of $\alpha\sim 0.25$ for atmosphere heights between sea-level and 
3~km, while $\alpha\sim 0.67$ for the 3--6~km layer. Toon \& Pollack (1976) argue that most visible spectral measurements indicate an average 
$\beta \approx 3 \pm 0.5$. The average values of the aerosol optical depth found for the SPM site show that $\beta_\mathrm{OP} \sim 2.7$ and 
$\beta_\mathrm{OIR} \sim 2.3$, which are thus consistent with expected values from these models. For the visible we derive an aerosol optical 
depth $\tau_\lambda=0.0001\lambda^{-0.72}$ and for the OIR $\tau_\lambda=0.0061\lambda^{-0.31}$ for the average values for the 2000--2008 period of 
AOT over San Pedro M\'artir. As is shown by Toon \& Pollack (1976) their global calculated aerosol optical depth spans a larger wavelength 
interval and it is expected that the OIR one that spans from 4300 to 21300~\AA\ would be a better representation of the mean AOT in a site. 
Considering all the AOT data from MODIS we derived for the SPM site an average slope $\alpha_\mathrm{OIR}$ of $0.31 \pm 0.06$ for the mean 
aerosol optical depth spectral data.


\subsection{AOT and Stellar Atmospheric Extinction}

In Figure~\ref{fig:figura7} spectral values of our mean and seasonal  AOT from MODIS data for the years 2000--2008, are compared with the SPM 
average atmospheric extinction curve ($\kappa_\lambda$) obtained by Schuster \& Parrao (2001) and Schuster et al. (2002) from stellar photometric 
observations for the years 1973--1999. Although $\tau_\lambda$ due to aerosol scattering and the atmospheric extinction $\kappa_\lambda$ cannot 
be directly related, since  the extinction over $3200 \lesssim \lambda \lesssim 6500$~\AA\ has the contributions from aerosol scattering, 
Rayleigh-Cabannes scattering and ozone absorption (see equation~1 in Schuster \& Parrao 2001, and references within), we can only check trends 
in the wavelength dependence. 

On the other hand, Schuster \& Parrao (2001) obtained for SPM a slope $\alpha_\mathrm{OP}$ of $0.87 \pm 0.04$ from their stellar photometric 
measurements during the years 1973--1999 for wavelengths from 0.3 to 1.1~$\mu$m. Their slope is somewhat larger than our average value of 
$0.72 \pm 0.05$ for 2000--2008, but note that our seasonal values vary from 0.62 to 0.81 (c.f. Table~\ref{tab:spectral}).  Stellar photometry 
measurements have been used to derive the aerosol scattering slope at several astronomical observatories. For the European Southern Observatory 
at La Silla (Chile) Burki et al. (1995) obtained a value of $\alpha_\mathrm{OP}$ of 1.39, while for Cerro Tololo Inter-American Observatory, Chile, 
Guti\'errez-Moreno, Cort\'es, \& Moreno (1982) found values of $\alpha_\mathrm{OP}$ varying from 0.2 to 2.6 during the years 1964--1980. Hayes 
\& Latham (1975) summarize in their Table~1 average values from stellar observations for several observatories: Le Houga 0.89, Boyden 0.78, 
Lick 0.49, Cerro Tololo 0.81, and Mount Hopkins 0.84, and derived a mean value of 0.81 for night-time stellar photometry. 

If we consider the values of $\alpha_\mathrm{OIR}$ which probably describe somewhat better the wavelength dependence of aerosol opacity because 
of the larger wavelength coverage, the mean value found for SPM $\alpha_\mathrm{aerosol}$ of $0.31 \pm 0.10$ and the seasonal values 0.27 (autumn) 
and 0.35 (winter) compare well with the Toon \& Pollack (1976) model for the atmosphere layer from 0 to 3~km, which probably indicates that at 
SPM this layer is dominant in the aerosol opacity.


%%%%%% FIGURA 7
  
\begin{figure}[!t]
\vspace{0.1cm}
\centering
\includegraphics[clip,width=0.98\columnwidth]{maraizafig7BN.eps}
\caption{Wavelength dependence of average atmospheric extinction ($\kappa_\lambda$) from Schuster 
\& Parrao (2001) represented with $\times$ symbols,  compared to the aerosol optical depth spectral 
values obtained from MODIS data for the San Pedro M\'artir observatory site. The color figure can 
be viewed online.}
\label{fig:figura7}
\vspace{0.3cm}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\vspace{0.15cm}

\section{Conclusions}

The aerosol optical depth or thickness (AOT) values, obtained from MODIS database for the San Pedro M\'artir (SPM) astronomical site in the 
period January 2000 to December 2008, show that the highest atmospheric transparency occurs during the  autumn months, with average values 
AOT of $0.089 \pm 0.013$ at 4700~\AA, $0.078 \pm 0.011$ at 5500~\AA, $0.072 \pm 0.010$ at 6600~\AA, and $0.056 \pm 0.008$ at 21300~\AA. This 
seasonal trend is consistent with the monthly behavior that shows the best transparency conditions in October and November in all the years 
studied. This result agrees with Schuster et al. (2002) finding that the best months for photometric observations at SPM are October and 
November, when the atmospheric extinction is quite low ($<$$\kappa_y$$>~\sim 0.12$) and the observing runs are mostly photometrically stable. 
So October and November are the months with higher atmospheric transparency and lowest atmospheric extinction. 

The annual behavior of MODIS AOT during the years 2000--2008 yields mean values of $0.147 \pm 0.103$, $0.128 \pm 0.090$, $0.115 \pm 0.081$, 
$0.087 \pm 0.066$ at 4700, 5500, 6600 and 21300~\AA, respectively. 

Wavelength dependence of the aerosol optical thickness in the interval from 0.47 to 2.1~$\mu$m is analyzed for all the MODIS data assuming a 
power-law behavior for the aerosol scattering ($\tau_\lambda \propto \lambda^\alpha$) and indicates a slope $\alpha_\mathrm{OIR}$ with values 
between 0.27 (autumn), where the best atmospheric transparency conditions occur, and 0.35 (winter) where conditions are worse; while the 4700 
to 6600~\AA\ slope $\alpha_\mathrm{OP}$ has values from 0.62 (autumn) to 0.82 (winter). We conclude that for periods with higher atmospheric 
transparency the slope $\alpha$ for aerosol scattering is smaller and steepens for periods with more opacity. 

We have also used the mean values for the AOT during the 2000--2008 studied period, which yields $\alpha_\mathrm{OIR} \sim 0.31 \pm 0.06$ 
($\tau_\lambda \sim 0.0061\lambda^{-0.31}$) and $\alpha_\mathrm{OP} \sim 0.72 \pm 0.08$ ($\tau_\lambda\sim 0.0001\lambda^{-0.72}$) for the San Pedro 
M\'artir location. The latter turns out to be somewhat smaller than the slope value obtained from stellar photometry by Schuster \& Parrao 
(2001) of 0.87 for wavelengths from 0.3 to 1.1~$\mu$m. Our results confirm that the atmospheric transparency at SPM is excellent and that the 
best observing conditions may occur in the months of October and November. 

Although we only obtained a partial climatology, since climatology requires a 20 year period, the results in the nine year period of MODIS 
data show that conditions over SPM are quite stable, possibly indicating that no dramatic changes in the AOT are expected. Nevertheless, 
further work with MODIS data is needed to obtain better estimates of the AOT, specially in the winter months of January and December, where 
the data are more scarce. The ambient aerosol optical thickness and the values of the aerosol spectral index of the San Pedro M\'artir in 
Baja California astronomical site found in this paper, corroborate its high atmospheric transparency and strengthen its quality among the 
prime astronomical sites in the world.  Finally, it is important that a long term ground-based campaign of aerosol optical depth measurements 
be carried out at SPM, for comparison with the MODIS AOT values obtained so far, and to establish the degree of confidence in the satellite 
measurements for this site.


\acknowledgements

We thank the staff at Observatorio Astron\'omico Nacional (Instituto de  Astronom\'ia, Universidad Nacional Aut\'onoma de M\'exico), the Solar 
Radiation Observatory (Instituto de Geof\'{\i}sica, Universidad Nacional Aut\'onoma de M\'exico), and the MODIS Aerosol NASA for providing valuable 
information and data. We thank W. Schuster and L. Parrao for kindly providing their extinction data and for helpful discussions. We also thank 
A. Leyva Contreras for helpful and valuable advice. We are indebted to A. Muhlia Vel\'azquez for his assistance and personnel at the Coordination 
of Remote Perception in Conabio (Mexico), specially, to A. Cervera Taboada and to G. L\'opez Salda\~na, for providing assistance with data 
processing. M. Araiza Quijano acknowledges Conacyt (Mexico) postdoctoral fellowship, and the Instituto de Astronom\'{\i}a, UNAM for providing 
the facilities and the academic environment for this work. We also thank the referee for his/her helpful comments.

\vspace{-0.1cm}

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\end{document}

