The optical depth (r) is the summation of extinction (scattering and absorption) by all the gases and pollutants of the atmosphere:

where nj is the altitude dependent concentration of the ( j ) gases and particles that attenuate radiation, each with an effective cross section (scattering and absorption) o). Retrievals of the optical depth from ground-based sensors generally employ two methods: (1) the Langley-plot slope method, and (2) measurements of absolute spectrally-resolved solar flux with a calibrated sun photometer. Each of these methods requires a clear cloudless day to make accurate measurements. The Langley method is a technique based on sun photometry introduced for the first time in November 1725, in France by Pierre Bouguer. This relative measure does not require an absolute calibration of the direct input of the sensor. However, retrievals of optical depths with the Langley method do not provide instantaneous information about the atmospheric optical depth since it requires measurements over a period of time, usually a morning or an afternoon. As a result, it assumes that both total atmospheric optical depth and sensor's sensitivity remain constant during the measurement period. Langley analysis is a linear regression of the natural logarithm (ln) of the signal that is measured vs. air mass (m). A graph of the natural logarithm of the signal vs. air mass falls along a straight line assuming that the atmosphere does not undergo a radical change or the aerosol loading does not change within the measurement time frame. The air mass is defined as the cosecant of the solar zenith angle for solar angles less than 75Q.Above this angle the spherical nature of the atmosphere has to be taken into account, and this involves a more involved calculation (Lenoble, 1993). Extending the straight line to where it crosses the y axis at m = 0 (zero air mass) yields the extraterrestrial constant, which is the solar flux at the top of the atmosphere. A time averaged extraterrestrial constant is referred to as the characterized Langley intercept for that particular instrument.

Figures 11.8 and 11.9 show two Langley plots derived from Brewer No. 112 during a 1999 summer intensive study at Riverside, California. The data is derived from the PS routine scans taken by the Brewer in the morning and afternoon at 340 nm. The Brewer PS routine looks directly at the sun in the morning and afternoon at various zenith angles to obtain the variables needed to determine the total optical depth. Notice the slight difference in the slopes of the two lines. The slopes are the total optical depths of the atmosphere. The morning slope shows a slightly higher optical depth (OD or $). Since the boundary layer increases with

Air mass

Figure 11.9 Afternoon Langley plot warming of the atmosphere, the pollutants tend to diffuse as the boundary layer becomes thicker and give a slightly lower OD ($). Other instruments, such as the UV Multi-filter Rotating Shadowband Radiometer (MFRSR), take considerably more data points and can produce Langley plots within an hour or so. This information can be valuable if the atmosphere varies more rapidly than expected.

Measurements taken with a calibrated sun photometer of absolute spectrally-resolved solar flux differ from the standard Langley method in that the extraterrestrial constant is used to directly calculate the total atmospheric optical depth providing instantaneous information about any changes.

Attenuation of a direct solar beam is described by the Beer-Lambert law:

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