This page's content and links are no longer actively maintained. It is available for reference purposes only.
ICP Website Curator: Robert B. Schmunk — NASA Official: Gavin A. Schmidt


Aerosols Study: Project Training

A More In-depth Understanding of how sunphotometers are used to determine optical depth

Basic concept: Since aerosols scatter sunlight, the larger morning and evening air masses create more scattering.

Small solid and liquid particles in the atmosphere, called aerosols, dissipate sunlight energy through Rayleigh scattering. Increase the number of particles along the sunlight's path or increasing the path length are two factors that can decrease the amount of energy reaching the earth's surface. Morning and evening sunlight experiences the most scattering because it passes through the greatest path length. As the sun's position approaches noon, the path length decreases, and there is less energy lost to the aerosols.

The measured voltages from the sunphotometer and air mass values determined from the time of day, along with a Langley Regression, determines the optical depth.

What is a "Langley Regression" or a "Langley Analysis"? What is the "Langley Method"? Who is Langley? And what is this strange device called a "sunphotometer"? How are all these things related?

What is the Langley Method?

The Langley Method is named after Samuel Pierpoint Langley, who worked at the Smithsonian Institution, and is based on his early work of the early 1900's to determine solar flux.

Langley found out that if we increase the amount of air molecules along the path of the solar beam, we decrease the amount of solar energy that can reach the surface. We can also decrease the amount of solar energy that reaches the surface by increasing the path length that the radiation has to go through.

It is this pathlength dependence that is used in the Langley Method.

Measurements are made at the earth's surface using a sun photometer for a period after sunrise and before sunset. The position of the sun also changes with time.

Visualize this:

At sunrise and sunset, the solar energy (sunlight) has to go through a greater path length. As the time approaches noon, the path the sunlight has to go through is shortened. The mass of air, or "air mass," is less. Air mass is 1 divided by the size of the Sun's angle above the horizon (m=1/sin)

Path lengths during the day
Path lengths during the day.

If you look at the figure above, you can see that the path length that the sunlight has to get through decreases from the time of sunrise to noon. As the path length decreases the air mass decreases and more sunlight reaches the surface increasing the intensity measured by your sunphotometer as a voltage. When more sunlight gets through, the intensity increases. So, there is a direct relation between intensity and airmass and that can be graphed.

The equation V=Voe-mt is used to relate the amount of energy reaching the earth's surface (V) to the two factors affecting the sunlight's transmission, specifically the air mass (m) and optical depth (t). (The term optical depth is used to represent the aerosol density.) So you have three unknowns: the voltage at the earth's surface, the air mass, and the optical depth. You use the sunphotometers to measure the surface voltage (V) and use the time of day to determine the air mass (m); these two measurements will allow you to determine the third unknown, which is the optical depth (t). The optical depth is the value you want to find because it allows you to compare the air quality of different locations.

V = Voe - mt

V = digital voltage reading on the sunphotometer

Vo = extraterrestrial constant

e = 2.71828

m = air mass

t = optical thickness, or optical depth NOTE:Use the langley regression along with your sunphotometer measurements to determine this value.

Using the natural log converts the exponential equation above to a linear representation, i.e. y = mx + b, which makes finding the optical depth easier.

log equations  
line equation: lnV vs Air Mass  

For the last step, remember that ln ex = x.
The last line gives an equation in linear form:

  • the x-axis is the air mass, m
  • The y-axis is the voltage measured at the earth's surface, lnV
  • the y-intercept gives the voltage at the top of the atmosphere, and is a constant value, lnVo
  • and (most importantly) the slope is the optical depth, t

A typical procedure requires measuring the voltage every 30 minutes for a few hours in the morning and repeating the measurements in the evening, before sundown. So the main idea is: plotting the natural log of the surface voltages as a function of air mass gives the optical depth for the day as the magnitude of the slope of the regression line.

Further Reading

An Inexpensive and Accurate Student Sun Photometer with Light-Emitting Diodes as Spectrally Selective Detectors.

Calibration and Data Collection With the GLOBE Sun Photometer

Characterization of LED-Based Sun Photometers for Use as GLOBE Instruments