Introduction

I have worked for many years with sun photometers, devices designed to measure the transmission of the atmosphere in narrow spectral regions using the sun as a light source.  In fact designing, constructing and acquiring sun photometry data was the topic of my dissertation research at the University of Arizona in 1971. I was the first to employ PIN-doped solid state detectors along with well blocked high quality interference filters to yield a very stable detection system.

Probably the most common application for a sun photometer is to establish the “degree of haziness”, or turbidity of the atmosphere, This in itself is a rough metric of air quality which can be used, with measurements made over a long time, to establish trends in air pollution, or perhaps to judge the degree of improvement in air quality following implementation of reductions in aerosol sources.

Recovery of the aerosol size distribution from sky/run photometry

With the use of stable sun photometer instruments one may readily make field measurements of the wavelength distribution of aerosol optical depth. From this it is possible to estimate the size probability distribution of the aerosols by using an inversion technique. However the information content is low and one can only get rough, rather smeared out estimations of the size distribution.  If, on the other hand, measurements of the angular dependence of sky radiance can be simultaneously made, then one can obtain good estimates of the aerosol size distribution function by inverting a combination of extinction and angular data. I have done some of the early work on developing this technique. Such radiometric measurements and attendant inversion techniques are now incorporated routinely in the global AERONET system of photometers.

Deriving vertical structure of aerosols  and their sources by sun photometry 

A rather novel use of sun photometers is to establish the vertical structure of aerosol layers in the atmosphere. This can be done in a number of ways, probably the most common of which is simply to mount the sun photometer on an aircraft and traverse up and down through the layers and differentiae the signal to derive the vertical profile of optical extinction coefficient. The author and colleagues used this method extensively in the 1970’s to derive the vertical distribution of Arctic Haze near Barrow, Alaska.  From these measurements, along with back trajectory analysis made from synoptic meteorological charts, it was deduced that the most probably source regions for the unidentified Arctic Haze was probably central Eurasia. 

In this manner, the author (Shaw, 1979) employed a portable sun photometer to deduce that aerosol clouds were transported across the Pacific Ocean from the Chinese mainland to the Hawaiian Islands.  The vertical structure of the haze layers was recovered by simply driving the instrument from sea level to the Mauna Loa Observatory and stopping every few miles to make measurements of turbidity and of altitude with a barometric altimeter.  Sky radiance was also determined from a photographic method and so it was possible by combining the two data sets to deduce that the aerosol particles in question were mainly in a mode one or two micrometers in diameter.  

Remarks on subtleties of Calibration

I decided to add a section on calibration because unrecognized problems with calibration often occur in practice, leading to inaccurate data, sometimes with spectacularly large error.

To establish a calibration for a sun photometer, one must determine in some manner what the instrument’s response would be for completely untenanted sunlight.  One way of doing this would be to take the instrument into space and have the astronauts determine the calibration constants by pointing the instrument directly at the sun.  This of course is very expensive and can only be done very occasionally.. Another, more practical and common, way is to employ the so-called Langley method.  Using the Beer-Lambert law for attenuation of light through an atmosphere of optical depth tau, the sun photometer signal voltage, V may be expressed as

V = Vo  exp (-tau * m)

Where m is the air mass, or atmospheric path length, expressed in path length for a vertical column.  This may be approximated by m = sec (z), where z is the sun’s zenith angle for a plane parallel atmosphere.    By taking the natural logarithm of equation 1,

ln (V) + ln (Vo) – tau * m

Thus, there is a linear relationship between variables ln (V) and m, with ordinate axis intercept Vo and slope –tau. This may be used to establish the optical depth tau along with the calibration zero air mass intercept Vo, simply by taking measurements over a range of air masses and assuming that the optical depth remains constant.  Figure 1 shows some actual data to illustrate the above linear relationship and extrapolation method.  The numbers on the graph correspond to the wavelength of light for the central pass band of the interference filters.

In the case where aerosol is time varying one cannot use the Langley method and calibration constants need to be established by some other method, for example by inter comparing with an identical instrument which has undergone previous, accurate Langley plot calibration.

It is frequently said that “quality” of a Langley plot may easily be judged by the closeness of fit to the linear regression curve.  If in fact the atmosphere has been stable during the measurement period, then the individual data points will fit the straight line regression to high accuracy.  If there is a drift in optical depth during the measurements, for example a build up during the day of air pollution, perhaps by photochemical conversion, then, so it is frequently claimed, the best fit line will be “curved” in some manner and not accurately fall along a straight line fit.  Indeed there are often times during which this is the case. When it occurs, obviously one must reject that particular day as a “calibration” day for using the Langley Method of extrapolation. 

However, it is also not only quite possible, but actually rather common, to have a situation in which a time varying turbidity can lead to surprisingly straight Langley plots, but which would, if used extrapolate an entirely incorrect estimate of the zero air mass intercept voltage. Such a situation occurs if the variation of optical depth with time is symmetric around the solar noon time. For instance you might have an air shed which undergoes systematic diurnal variation, for example pollution building up in the morning hour, then eroding away in the afternoon hours by being lofted above surrounding mountains or being taken out of the area by upper winds.

To provide an example of this insidious and quite surprising often unrecognized error source, we have modeled a Langley plot for a hypothetical atmosphere in which turbidity varies parabolic around the solar noon time.  

Figure 1: Langley Plot

Note that even though there is a strong diurnal variation of turbidity throughout the day, the Langley plot is surprisingly linear.  The zero air mass intercept so extrapolated is in error, in this case by about ten percent!!

The only way to safely utilize the Langley Method, in our opinion, is to ship the instrument to a mountain observatory with excellent and low turbidity conditions, for example the Mauna Loa Observatory at an altitude of 3.4 km and in the middle of the Pacific Ocean.

Solar Spectral Irradiance

In principle the Langley method can be utilized to extrapolate spectral measurements of the sun’s irradiance to its extraterrestrial value. There in fact is much interest in establishing the sun’s spectral irradiance and in absolute physical units. 

This method was first used and developed by the Smithsonian Astrophysical Laboratory under its Director S. Langley and Charles Greely Abbott and over the years from 1920 to 1945.  The Smithsonian program eventually incorporated a network of high mountain spectrometers in an attempt to search for small variations in spectral irradiance that might affect global crop growth. No such variations were found, except for possible variations at or below the limit of accuracy, which was about 1%.

Though the Smithsonian and other programs carried out since, managed to estimate the solar spectral irradiance for the sun, the absolute values often disagree, by 5 % or more at blue and near ultraviolet wavelengths.  This disagreement is associated with many subtle error sources, some systematic and hidden, that affect absolute radiometry.  For example, the irradiance values are often tied to standard lamps, which have been calibrated at Laboratories by measuring Planckian radiation from molten gold, or similar methods.

We have carried out our own investigations of spectral solar irradiance at Mauna Loa, using a filter wheel photometer. In one study (Shaw, 1982) we utilized a year of solar radiation measurements to estimate the accuracy by which one can extrapolate through the atmosphere using the Langley Method.  If the sun’s irradiance remained constant over this period, than the root mean square (rms) deviations of the extrapolated value of zero air mass intercepts may provide an estimate of the accuracy of extrapolation.  The rms error of atmospheric extrapolation varied from 0.3 to about 1 percent, though it could have been lowered by more careful selection of the days used and time periods chosen for extrapolation, for example by rejecting data during which times aerosol concentration increased at the station, or during days in which sub visible cirrus or high haze layers were present. We estimate that by carefully selecting time periods for the optimal seeing conditions at Mauna Loa, one can routinely use the Langley method to derive the zero air mass intercepts to several tenths of one percent. 

The sun’s spectral irradiance in absolute units was also calculated for each of the filter wavelengths by comparing to a standard type FEL 1000 watt quartz iodide lamp.  In our case the lamps were cross referenced to a semi standard lamp brought from the National Standards Laboratory in Washington and the estimated calibration uncertainty is +/- 2%.   Our values of solar spectral irradiance were, except in two cases, within 1% of the values reported by Labs and Nickel (1968), except at the wavelength bands redder than 790 nm, which are suspected to be slightly contaminated by water vapor absorption bands. At 416 nm our value of irradiance is 4% larger than L&N, while at 460 nm our value was 7 percent larger. 

At one wavelength, we performed an elaborate and very thorough absolute calibration that bypassed the use of standard lamp sources. We used a several watt tunable dye laser and measured the absolute voltage from the detector/filter assembly, along with the absolute power from the laser. The power was directly measured by using a Cavity Radiometer developed at the World Radiation Laboratory at Davos. Carrying out this procedure, wavelength by wavelength, and over the 10 nm wide spectral band pass, provided the calibration constant for the detector/filter photometer. Our extrapolated value for spectral solar irradiance at 500 nm, using measurements from Mauna Loa, was two percent higher than Lab’s and Nickle’s tabulation.   

References:

Shaw, G. E., J. A. Reagan, and B. M. Herman, Investigations of atmospheric extinction using direct solar radiation measurements made with multiple wavelength radiometer, J. Appl. Meteor., 12 374, 1973

Shaw, G. E., Error analysis of multi wavelength sun photometry, Pageoph., 114, 1, 1976

Shaw, G. E., Solar spectral irradiance and atmospheric transmission at Mauna Loa Observatory, Applied Optics, 21, 2006m 1982.