The standard algorithm used for determining total ozone with the Brewer instrument is a DOAS technique using radiation measured at four of the operational UV wavelengths, (As shown in Fig. 6.3): 310.1 nm (A = 2), 313.5 nm (A = 3), 316.8 nm (A = 4), and 320.0 nm (A = 5). Bandpasses for the slits are approximately triangular in shape (Grobner et al., 1998) with a full-width-half intensity (FWHI) of about 0.6 nm (Kerr, 2002). The DOAS method for measuring total ozone is based on the following equation (Kerr et al., 1981), which quantifies the intensity of direct solar radiation at the earth's surface:
log® = log(/oi) - Pi m X p/p0 - nsec (SZA) - aÀÛ3 M (6.2)
where h is the measured intensity of radiation at wavelength A. Io i is the extraterrestrial intensity at wavelength A.
Pi is the Rayleigh scattering coefficient at X.
m is the effective pathlength of direct radiation through air.
p is the pressure at the station.
pois standard pressure (1,013.25 millibars).
tx is the aerosol optical depth at X.
sec (SZA) is the secant of the solar zenith angle (SZA).
ax is the ozone absorption coefficient at X.
O3 is the column amount of atmospheric ozone.
H is the ratio of the effective pathlength of direct radiation through ozone to the vertical path.
The intensity of radiation at the four operational wavelengths over the 10 nm range is represented by the 4 I\ values shown in Eq. (6.2). The measurement of ozone takes advantage of the curvature of ozone absorption as a function of wavelength over the wavelength range (Fig. 6.3). The four equations (X = 2 - 5) are linearly combined and rearranged to yield the following:
where F = log (I2) - 0.5 log (I3) - 2.2 log (I4) +1.7 log (I5)
F0=log (I02) - 0.5 log (I03) - 2.2 log (Io4) +1.7 log (I05) Ap = p2 - 0.5 P3 - 2.2 pA +1.7 P5 AT=tô2 - 0.5 TÔ3 - 2.2 TÔ4 +1.7 TÔ5 ~ 0 Aa = a2 - 0.5 a3 — 2.2 a4 +1.7 a5
The linear combination is weighted to minimize effects of small shifts in wavelength (i.e., AFo/AX is near a stationary point) and to eliminate SO2 absorption. The weighting also makes any function linear with wavelength equal to zero (i.e., X2 - 0.5A3 - 1.7A4 + 2.2A5 = 0). Thus aerosol scattering (ArS), which is approximately linear with wavelength over the relatively small wavelength range, becomes negligible in Eq. (6.3). The effects of Rayleigh scattering (APm) in Eq. (6.3) are calculated using the Rayleigh scattering coefficients of Bates (1984). The amount of total ozone is then readily calculated from the equation using O3 = (Fo - F -Apm)/Aa/u provided values for Fo and Aa are known. The precision over a long period of time for a direct sun measurement made with a well-calibrated and well-maintained Brewer instrument is demonstrated to be better than +1% (Fioletov et al., 2005). Values of Fo and Aa (calibration constants) are unique for each instrument and depend on the detailed band passes of the slits of each instrument. All instruments in operation require the determination of the calibration constants. Determination of the calibration constants is discussed further in Section 6.5.2.
The Brewer instrument is also used to derive total ozone from measurements of polarized radiation scattered from the zenith sky. The zenith radiation measured at the four wavelengths is weighted to yield the value Fzs, in the same manner as F for direct sun shown in Eq. (6.3). Many pairs of direct sun and zenith sky observations taken over a period of more than a year are used to establish a statistical relationship that relates Fzs as a function of Fo, total ozone (derived from direct sun data), and airmass (^). The measurement pairs are made under a wide range of total ozone and airmass values. Once the relationship is established, total ozone can be determined from a measurement of Fzs made when the sun is not available.
The precision of the zenith sky measurement is not as good as that for the direct sun (Dobson, 1957; Brewer and Kerr, 1973) and is observed to be about ± 2% under most conditions without heavy clouds provided the zenith sky algorithm has been derived for the specified instrument and location. Radiation polarized parallel to the solar plane is used since it has been shown that this radiation is less sensitive to the presence of thin clouds (Brewer and Kerr, 1973). When heavy convective clouds are present, the apparent total ozone can increase substantially (Fioletov et al., 1997; Mayer et al., 1998; Kerr and Davis, 2007). This is likely caused by enhanced absorption due to multiple scattering through ozone within the clouds.
Total ozone derived from zenith sky measurements also depends on the vertical distribution of ozone, particularly when the SZA is large. For example, the majority of zenith radiation passes vertically through a layer of ozone near the ground since most of the radiation is scattered above the layer. However, for a layer near the top of the atmosphere, the effective pathlength is relatively longer since most of the scattering occurs below the layer and radiation from the sun that is scattered toward the instrument passes through the layer obliquely.
Total ozone is also derived from measurements of global radiation (Fioletov et al., 1997; Kerr and Davis, 2007) and measurements using the focused sun (Josefsson, 1992) or moon (Kerr, 1989a) as a light source. Measurements using global irradiance are useful for situations when the direct sun is not available. Focused sun measurements are used at high latitudes at times of the year when the solar elevation does not reach 15 ".Measurements using the moon as a light source are useful for obtaining data when the sun is below the horizon. This is particularly beneficial for obtaining data from high latitudes during winter when the sun is absent most of the time.
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