# Hands On Physics

### Haze Concepts HAZE FORMULA

Every TERC VHS-1 has its own distinctive ET constant. This calibration number permits you to determine what scientists call the Aerosol Optical Thickness (AOT) of the atmosphere. AOT provides an excellent haze index. Even though the ET constant of different instruments may vary, all instruments should give very similar AOTs.

The formula for AOT is:

#### AOT = (ln ET - ln signal-((0.139 x m) x (p/1013.25) x m))/m

where,
• ln ET is the ln of the extraterrestrial constant for the TERC VHS-1,
• ln signal is the ln of the signal measured by the TERC VHS-1,
• 0.117 is the AOT caused by Rayleigh scattering in the atmosphere at 525 nm,
• m is the air mass, and
• p is the atmospheric pressure for your location in millibars.

If your barometer indicates inches of mercury instead of millibars, change (p/1013.25) to (p/29.92). If you don't have a barometer, you can use the U.S. Standard Atmosphere to estimate the mean p for your location's elevation above sea level (you can round the numbers to the nearest decimal point without affecting your AOT results):

Elevation (meters) Pressure (millibars) 0 1013.25 500 954.61 1000 898.76 1500 845.59 2000 795.01 2500 746.91 3000 701.21 3500 657.80 4000 616.60 4500 577.52 5000 540.48

(From "U.S. Standard Atmosphere, 1976" (National Oceanic and Atmospheric Administration, National Aeronautics and Space Administration and the U.S. Air Force, 1976) as published in "Handbook of Chemistry and Physics," CRC Press, Inc., p. F144, 1987.)

Notice that the AOT formula subtracts the effect on optical depth caused by Rayleigh scattering from molecules of air. This is why the formula can provide the optical depth caused only by aerosols and particles (tiny water droplets, smoke, pollen, dust, salt, sulfates, etc.).

Incidentally, if you are interested in math, you might wonder why the terms of the AOT formula are divided by the air mass. This permits measurements made at different times or by instruments in different locations to be compared by adjusting all measurements by all instruments for the air mass directly overhead (m = 1). This method works very well if the air is stable between the instrument and the Sun. But if the path of sunlight moves over a polluted or hazy region, the AOT you measure will not accurately reflect the air mass directly over your head.

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