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It is known that the complete information about the state of polarization of light at the certain wavelength can be described as a fourcomponent Stokes vector, I = [I, Q, U, V], (Chandrasekhar, 1960). The Stokes component, I, represents the total intensity, Q and U the linear polarization, and V the circular polarization of the light beam. Except a limited number of Polarization Measuring Devices (PMDs) on GOME, SCIAMACHY, and GOME2, which provide broadband polarization information for the purpose of polarization correction (Hasekamp et al., 2002), most of the satellitebased highspectralresolution UV remote sensors such as GOME and OMPS only measure the first Stokes component.
To display the errors induced by neglecting the polarization in the UV radiance caculation under clearsky conditions, we calculate the TOA normalized radiance by using both the vector model and scalar model of the UNLVRTM for two different solar/viewing geometries. The midlatitude summer atmospheric profile is assumed. Figure 2 compares the TOA normalized radiances calculated from vector model and scalar model. In this case, the scalar approximation of radiative transfer model in UV region can overestimate the TOA normalized radiance by up to 3% at the scattering angle of Θ = 120° (solar zenith angle, viewing zenith angle, and relative azimuth angle are 30°, 30°, and 0°, respectively); and, by more than 8.4% at the scattering angle of Θ = 90° (solar zenith angle, viewing zenith angle, and relative azimuth angle are 60°, 30°, and 0°, respectively). The reason is that the maximum value of degrees of linear polarization of Rayleigh scattering is at the scattering angles near 90° (Wang et al., 2014). The polarization at the scattering angle near 90° is much stronger than at any other scattering angles. Just as Mishchenko et al. (1994) pointed out, the errors of scalar approximation in the case of Rayleigh scattering are especially significant when the scattering angle is equal or close to 90°. The results clearly manifest the importance of using a vector radiative transfer model for the radiance calculation in UV region.
Figure 2. (a) Comparison of TOA normalized radiances calculated from the vector model and scalar approximation and (b) their relative differences. The calculations are for solar zenith angles (SZA) 30° and 60°. The satellite viewing angle is assumed to be 30° and the relative azimuth angle is 0°. See details in the text.

To avoid very complicated calculations of electronic transitions, numerous measurements of the absorption crosssections of gases in the UV and visible regions have been performed in laboratory experiments. Normally, the measurement temperatures are selected to be those most useful in atmospheric applications and those values at –70, –55, –45, –30, 0, and +25°C are selected in the work of Bass and Paur (1985). In order to extend the use of these data, a set of quadratic coefficients for the following equation can be applied to calculate the ozone absorption coefficient α at an arbitrary temperature t, in Centigrade, at each wavelength,
$$\alpha = {C_0} + {C_1}t + {C_2}{t^2},$$ (1) where t is the temperature in Centigrade, C_{0} is the ozone absorption coefficient at 0°C, C_{1} is the linear temperature correction coefficient, and C_{2} is quadratic temperature correction coefficient. The quadratic coefficients are calculated from all the available spectra.
In UNLVRTM, the ozone absorption crosssection data with a spectral resolution of 0.01 nm are from the Smithsonian Astrophysical Observatory (SAO), and the absorption crosssections of other gases and spectroscopic line parameters are from the HITRAN2012 database (Orphal and Chance, 2003; Rothman et al., 2013; Wang et al., 2014). It can be seen clearly from Fig. 3 that the ozone crosssections in 300–380nm region (Huggins bands) consist of a lot of individual extending peaks and show a strong temperature dependence.
The main absorber of UV radiation in the atmosphere is ozone. Other trace gases such as NO_{2}, SO_{2}, and O_{2} also make contributions to the UV absorption. Figure 4 shows the absorption optical depths of different gases in UV region. The calculation is carried out by using UNLVRTM for the midlatitude summer atmospheric profile (McClatchey et al., 1972). It is shown that the ozone absorption optical depth is dominant for wavelengths less than 340 nm, and the absorption of NO_{2} and O_{2} become much stronger than that of ozone for wavelengths larger than 340 nm, although the value of total optical depth is small.
Figure 4. The absorption optical depth of different gases in UV region. The calculation is for the midlatitude summer atmospheric profile.
If only ozone is considered in the simulation of radiative transfer model (e.g., TOMRAD), the total absorption optical depth can be underestimated. To evaluate the bias introduced by ignoring the effects of other absorption gases, two tests are carried out by using UNLVRTM. In the first test, only ozone is considered and in the second one, ozone and other absorption gases, such as NO_{2}, SO_{2}, O_{2}, HCHO, and so on as labeled in Fig. 4 are all considered. Figure 5 shows the relative difference of TOA reflected radiance calculated for both tests. It is clear to see that the simulated TOA reflected radiance is overestimated, especially for wavelengths larger than 340 nm if only ozone is considered in the simulation of the radiative transfer model.

The most widely used approximation assumes that the surface is an Lambertian type, which reflects light isotropically. Such an assumption greatly reduces the amount of computer time. Coulson et al. (1960) pointed out that both the intensity and polarization fields of skylight are sensitive to the reflectance of the Lambertian surface, solar zenith angle, and direction in which the skylight is observed. To investigate the effects of surface reflectance on reflected radiance, we carry out a simulation for the surface reflectance fixed at 0.05 for all wavelengths in UV region, and then we carry out additional simulations by assuming different perturbations, 5%, 10%, and 20%, to the surface reflectance. Figure 6 shows the effects of surface reflectance uncertainties on TOA normalized radiances. The comparison is shown on the left panel. The right panel is the error bar for reflectance variation of 20%. Given a 5% uncertainty associated with surface reflectance, the TOA normalized radiances are not very sensitive (with relative difference less than 2%) to the surface reflectance for wavelengths less than about 330 nm, because less light can reach the surface due to the strong absorption by ozone at these wavelengths (Figs. 6a, c). The change of surface reflectance does not significantly influence the reflected radiance. However, for wavelength larger than 330 nm, the TOA reflected radiances are much sensitive (with relative difference larger than 2%) to the change of surface reflectance (Figs. 6b, c), because the light can reach the surface. In addition, we can see that the errors increase with increasing of wavelengths (Figs. 6a–c). In the simulation, the surface reflectance value at 331 nm is used for all wavelengths by following the TOMRAD simulation (Seftor et al., 2014). However, these results clearly illustrate that the assumption of a fixed surface reflectance within UV region may cause significant errors, especially for wavelength larger than 330 nm.

The problem of wavelength inaccuracy is far from being trivial. For example, a very small wavelength shift (WS) in Raman spectrum may cause an unidentified different spectrum during an experiment. The result of such a situation is that the instrument needs to be recalibrated and the entire experiment is repeated. Although the accuracy requirements of the remote sensor on satellite are not so high, the accurate wavelength calibration is extremely important and indispensable. This is particularly true when we validate the satellite measurements via a forward model. The calibrated wavelength should be used as inputs to the radiative transfer model and the spectral resolution of the instrument must be taken into account in calculation of the radiative transfer model. Unfortunately, there are only few laboratory measurements at very high resolution (0.01 nm or better) and with very accurate wavelength calibration (0.01 nm or better) according to Orphal and Chance (2003).
To figure out the influence of wavelength shifts on the simulated TOA reflected radiance for different spectral resolutions (observed by satellite instruments with different full width at half maximum, FWHM), we carry out two simulation tests with different FWHM values of 0.2 and 0.4 nm, respectively, in the 300–380nm region. As shown in Fig. 7, changes in the ozone spectrum for different WSs are very sensitive to the spectral resolution. In the 300–380nm region, the changes in the ozone spectrum for different WSs are resolution dependent. At a lower resolution, a WS of 0.05 nm introduces radiance changes of up to 9% and even a shift of only 0.01 nm still introduces radiance changes of up to 1.5%.