**Atmospheric Visibility in Grand
Canyon**

**and Northern Arizona**

**Andrew P. Odell**

**Department of
Civil and Environmental Engineering,**

**Northern Arizona University,
**

**ABSTRACT: **

**The opportunity to do this
could lie in astronomical data (extinction coefficients) obtained at Lowell Observatory since the 1950’s when photoelectric
photometry began on Mars Hill west of **

**We have found strong
correlation between visibility as determined with a nephelometer at Sycamore
Canyon (17 miles west of Flagstaff) and also on the south
rim of Grand
Canyon (Hance site,
56 miles NNW of Flagstaff) and the extinction coefficients determined at
Lowell Observatory.**

**I. INTRODUCTION**

Grand Canyon and

Fortuitously, Lowell Observatory,
located on the west edge of

Section II reviews the
astronomical data available for this task, and Section III summarizes the
visibility measurements available at the

**Fig 1**: These
three photos show the view NNW from Desert View toward

From: http://vista.cira.colostate.edu/Datawarehouse/IMPROVE/Data/Photos/GRCT/Html/1Spectrum_Series.htm

**II. ASTRONOMICAL EXTINCTION**

To measure the brightness of a star, astronomers make observations of standard stars (ones of known brightness) at different altitudes above the horizon. One expects that the stellar magnitude (a logarithmic function of signal) would vary linearly with secant of the zenith angle. The slope of this line is called the extinction coefficient, and the intercept yields the instrumental sensitivity correction factor.

For the past 50 years, these measurements have been made at Lowell Observatory on most clear nights with their 21” telescope (see Fig. 2). Fig. 3 shows a plot for one standard star; the magnitude in each of two filters as a function of the secant of the zenith angle. The extinction coefficient is the slope of that line.

The star becomes fainter as it moves toward the horizon for several reasons: scattering and absorption by molecules (known) and aerosols. For the purpose here, we want to isolate just the particle component, due primarily to scattering.

Download data here

**Fig 2:** 21” telescope
at Lowell Observatory.
**Fig 3: **Extinction
coefficients for two wavelengths.

**III. VISIBILITY DATA**

There are three methods of measuring visibility, from three different sites near Grand Canyon National Park: nephelometers (Fig. 4) draw air into a chamber and measure the light scattered by particles; aerosol samplers (Fig. 5) draw air though a filter paper, which is then weighed; and transmissometers (Fig. 6) send light over a large distance and measure the attenuation of the beam.

The first two methods have been in operation for approximately ten years at Indian Gardens in the Grand Canyon and on the rim south of Hance Canyon (run by NPS), and also at the head of Sycamore Canyon near Garland Prairie (run by ADEQ and USFS). A transmissometer is still in operation between Phantom Ranch and Yavapai Point.

**Fig
4 (left): **Nephelometer at the head of

**Fig
5 (center):** The aerosol sampler
located at the head of

**Fig
6 (right):** Transmissometer located at Yavapai Point
looking at a light source located at Phantom Ranch. A photometer on the back of the telescope
measures the light level, and the extinction is calculated.

**IV. ANALYSIS**

The unfortunate part of
statistics is that one can only prove a **lack** of correlation, and never
the existence of one. Press et al. (p.
454) put it this way: “...the curse of statistics, that it can never prove
things, only disprove them!” One can
only estimate the likelihood that a correlation is not a result of random
chance.

The nephelometer measurements
(light scattered by aerosols) might be expected to most likely correlate with
Lowell extinction, first at the Sycamore site (about 17 miles west of the
Observatory), but also the Hance site (about 50 miles north and 17 miles west
of the Observatory). Hence the

The normal method of estimating correlation is through a linear least squares fit, and the correlation coefficient. The probability of a correlation can be computed based on the assumption of a binormal distribution of the deviations from the line. In the case of the nephelometer and Lowell extinction, there are a substantial number of outliers due to local conditions at each site (forest fires and controlled burns, as well as varying wind directions), rather than uncertainties.

The result of these outliers is that the values of the probabilities are not reliable, but the relative values probably are. The linear fit is also affected by these outliers, and a better method (more robust) is to use a fit based on minimizing the absolute-value of the distances of points from the line, rather than the square of the distances.

We have carried out probability
estimates for the correlation of the Sycamore, Hance, and

**V. RESULTS**

Fig. 7 shows the probability of
finding such a level of correlation by random chance as a function of time
offset, for the Hance nephelometer data and

A similar correlation pattern was
obtained between the Sycamore nephelometer measurements and

**Fig
7 (left):** The probability of correlation by random chance
between the nephelometer data from Hance and

**Fig 8 (right):** The comparison
of the Hance nephelometer data with the Lowell Extinction data for an offset of
+4 hours. The nephelometer values are
Bsp = **<****σ****N>** (mean particle cross-section times particle density;
per 103 km horizontal distance). The **τ**** **=**
∫****σ****Nds** (Bsp as above,
integrated to the top of the earth’s atmosphere) at 550 nm (y). The green line is a linear
least-absolute-distance fit.

**VI. CONCLUSIONS**

It is quite clear from Fig. 7 that
the relationship between astronomical extinction and visibility at the Grand
Canyon Hance Site (as well as

**References**

VIEWS WEBSITE: http://vista.cira.colostate.edu/views/

IMPROVE WEBSITE: http://vista.cira.colostate.edu/improve/

Bohren, C. F. and E. E. Clothiaux, 2004. *Fundamentals of Atmospheric Radiation. *Wiley-VCH
Verlag GmbH & Co. KGaA, Weinheim.

Bohren, C. F. and D. R. Huffman, 1983. *Absorption and Scattering of Light by
Small Particles*. John Wiley &
Sons,

Lockwood, W. E., Lowell Observatory,* private
communication.*

Press, W. H. *et al.,* 1986. *Numerical Recipes – The Art of Scientific
Computing.*

**Acknowledgements**

We would like to thank Wes Lockwood of Lowell Observatory for
making his extinction measurements available.
We also thank William Auberle of