Atmospheric Visibility in Grand Canyon

and Northern Arizona

Andrew P. Odell

Department of Civil and Environmental Engineering,

Northern Arizona University, Flagstaff, AZ 86011


ABSTRACT:  Grand Canyon National Park has experienced increased haze that obscures the views and disappoints visitors. Visibility monitoring began in 1998, so it would be of interest to extend visibility information to an earlier time, before power plants and increased automobile traffic came to the area.


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 Flagstaff.


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.




Grand Canyon and Northern Arizona have traditionally had among the clearest skies of any locale on earth.  For this and other reasons, Percival Lowell chose to locate his observatory here in 1894. However, in the last 25 years, much of this visibility has been compromised, especially at Grand Canyon National Park, as anthropogenic haze has obscured the panoramic views (see Fig. 1).  Monitoring of visibility began at the Park in the late 1990’s, but it would be most valuable to to extend the measurements back to a time when smog from nearby cities and local automobile traffic, as well as coal-fired power plants in Northern Arizona had not yet impacted the views.


Fortuitously, Lowell Observatory, located on the west edge of Flagstaff, AZ was a pioneer in the field of photoelectric photometry, this being put on a firm basis during the 1950’s.  In the course of measuring the brightness of stars, one must establish the effects of the earth’s atmosphere.  It is potentially possible to establish a relationship between this transparency and visibility at the Grand Canyon and elsewhere on the Colorado Plateau, and hence produce a tool to derive estimates of historical visibility at the Canyon.


Section II reviews the astronomical data available for this task, and Section III summarizes the visibility measurements available at the Grand Canyon.  Section IV gives a summary of the correlation between the two types of data, and Section V attempts to draw conclusions about the process.


Fig 1: These three photos show the view NNW from Desert View toward  Mt. Trumbull, about 75 miles away, at noon on different days.  Haze scatters light out of the beam from a distant vista, while also scattering sunlight into the beam.  The upper left picture was taken on a day with visual range Vr ~ 135 miles – about 10% of days are as clear or clearer than this.  The center picture was taken on a day with Vr ~ 100 miles, about median clarity.  The lower right on a day with Vr ~ 65 miles; about 10% of days are hazier than this day.






            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.





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 Hance Canyon.  Air is drawn into the chamber, a light beam passed through it, and a detector measures the light scattered at right angle out of the beam.  The particle scattering optical depth per 1000 km is calculated.

Fig 5 (center): The aerosol sampler located at the head of Hance Canyon on the rim of Grand Canyon.  This device draws air though a filter paper, and the change in weight yields the mass of particulates per cubic meter of air.  These samplers are run for 24 hours every three days.

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.




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 Lowell measurements were corrected for molecular (Rayleigh) scattering and known absorption (O3); molecular and particle absorption are expected to be small in the visible part of the spectrum.


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 Indian Gardens nephelometers with the Lowell extinction, and varying the offset time by 2-hour steps, to take into account the possibility of a travel-lag-time between sites. This also provides information on the case of data not expected to be correlated.





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 Lowell extinction measure.  Positive offset indicates time later at Lowell than Hance.  Note that the probability scale is logarithmic, and that the high probability of correlation offset by +4 hours has a value of less than one in a trillion.  We think that this value is unreliable, as discussed above (because of non-Gaussian statistics) but that relative to the surrounding values, it indicates a most likely correlation.


A similar correlation pattern was obtained between the Sycamore nephelometer measurements and Lowell extinction, with about the same time offset.  This would indicate the aerosols move eastward at about four miles per hour.  There was a much smaller correlation between the Indian Gardens nephelometer, and well as between the aerosol sampler and transmissometer data and Lowell Observatory.  This is probably a result of the fact that the Lowell telescope looks upward, not downward.













Fig 7 (left):  The probability of correlation by random chance between the nephelometer data from Hance and Lowell extinction data, as a function of offset in time. The peak is at +4 hours (Lowell after Hance).  The broad peak indicates that conditions change over about a 24-hour timescale.  Note that the abscissa is a logarithmic scale, to show the true range of values.  We do not believe the actual numbers (see text), but rather that there is highly significant correlation at +4 hours offset..

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 = <σN> (mean particle cross-section times particle density; per 103 km horizontal distance).  The Lowell extinction values are optical depth due to particles,  τ =σNds  (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. 





It is quite clear from Fig. 7 that the relationship between astronomical extinction and visibility at the Grand Canyon Hance Site (as well as Sycamore Canyon) DOES exist, and allows for the estimation of  extinction during a time when it was not being directly monitored.  Thus we have a method to determine the distribution of days with certain clarity at Grand Canyon over the past fifty years.






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, New York.

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

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





We would like to thank Wes Lockwood of Lowell Observatory for making his extinction measurements available.  We also thank William Auberle of Northern Arizona University and Carl Bowman of Grand Canyon National Park for their guidance, discussions and encouragement.