## Langley Analysis

While the laboratory calibrations and characterizations of the UV-MFRSR instruments were routinely performed, an alternative technique that has been used for many decades in various applications is the Langley plot method (Shaw, 1982; Thomason et al., 1983; Wilson and Forgan, 1995; Slusser et al., 2000). The Langley plot is used to provide more frequent calibrations of both the UV and VIS MFRSRs. The Langley method is based on the Beer-Lambert law, which describes the attenuation of the sun's direct-beam monochromatic radiation passing through the earth's atmosphere and is expressed mathematically (Thomason et al., 1983; Wilson and Forgan, 1995) as:

In Eq. (8.1), is the direct normal irradiance at the ground at wavelength A, R2

denotes a correction for the earth-sun distance at the time of measurement, I0 ^ represents the extraterrestrial irradiance, Tx,i is the optical depth for the i-th air component, and mt stands for the air mass of the i-th air component through the atmosphere. Taking the natural logarithm of both sides, we have lnIx= ln(R. (8.2)

Provided that the irradiance is obtained by applying a calibration factor to the voltage output of the radiometer, the Beer-Lambert law can also be applied to the voltage of the instrument measurement. For the raw voltage output of the detector the formula is:

In Eq. (8.3), Vx is the measured voltage at wavelength A, and V0,x represents the voltage the detector could measure oriented normal to the sun at wavelength A outside the earth's atmosphere at one Astronomical Unit. Assuming that the optical depth remains constant over a period of time when the air mass, which is a function of SZA, changes significantly, the Langley analysis method determines the V0, x by extrapolating voltage intercept at zero air mass when a linear fit to the logarithm of the measured voltage versus air mass is performed. Since the values of R and I0,x can be accurately estimated (Lean 1991; Lean et al., 1997), a calibration factor O to convert the measured voltage at wavelength A into irradiance can be determined as:

The calibrated irradiance, I^f, over the filter pass-band is obtained by multiplying the detector voltage measured at the ground by the calibration factor c^p (Bigelow et al., 1998). The calibration factor is determined using the filter-weighted integrations of I0,x and V0,x as follows (Slusser et al., 2000):

where Fx is the filter function or spectral response function of the filter. After the direct and diffuse components of the voltage have been corrected for an ideal cosine angular response, the Langley analysis based on the objective algorithms (Harrison and Michalsky, 1994) is performed to determine V0,Obtaining the correct V0 is essential in calibration. The V0 values are generated for morning and afternoons that supply at least 12 clear-sky measurements to the algorithm. The V0 values are collected over air mass ranges that depend on the wavelength of the channel. For example, for the 300 nm through the 325 nm channels, the measurements for the direct beam voltages for an air mass range of 1.2 to 2.2 are used, while for the 337 nm and 368 nm channels, an air mass range between 1.5 and 3.0 is used. All the morning V0 values deemed to be measured under clear sky for a given instrument at a given site are used as the ordinate in a linear regression routine using the air mass as the abscissa. The V0 for the day is the offset derived from the regression routine.

Comparisons from previous studies of sun photometer calibration using the Langley analysis and the standard lamp in (Schmid and Wehrli, 1995; Schmid et al., 1998; Janson et al., 2004) show that the Langley analysis calibration is superior to the lamp calibration when the analysis is performed under very clear atmospheric conditions. However, the Langley calibration introduces more uncertainties at shorter wavelengths (around 300 nm) because the signals are weak. The Langley method cannot be applied in conditions where the Beer-Lambert law is not applicable such as over broad spectral bandpasses, or where multiple scattering may introduce path radiance into the detector's field of view. Other limitations of the Langley calibration method are discussed in Wilson and Forgan (1995), and Schmid et al. (1998). The combination of both types of calibration serve as an additional means of quality control; long term drifts from lamp calibrations can be detected by comparison with the Langley values whereas unresolved cloudiness in the Langley calibration data may be signaled by comparison with the lamp values. Thus, the use of a combination of both Langley calibration and lamp calibration is recommended to maintain a long term accurate calibration (Schmid and Wehrli, 1995). Figure 8.7 shows the results of the Langley analysis for two UV-MFRSR instruments deployed at Mauna Loa, HI. In the upper plot, 300 nm V0s are shown, which are characteristically noisy due to a relatively low signal level as compared to the 305 nm channel data displayed in the lower plot.