Abstract
Abstract. The Differential Optical Absorption Spectroscopy (DOAS) technique is widely used to retrieve amounts of atmospheric species from measurements of the direct solar light transmitted through the Earth's atmosphere as well as of the solar light scattered in the atmosphere or reflected from the Earth's surface. For the transmitted direct solar light the theoretical basis of the DOAS technique represented by the Beer-Lambert law is well studied. In contrast, scarcely investigated is the theoretical basis and validity range of the DOAS method for those cases where the contribution of the multiple scattering processes is not negligible. Our study is intended to fill this gap by means of a theoretical investigation of the applicability of the DOAS technique for the retrieval of amounts of atmospheric species from observations of the scattered solar light with a non-negligible contribution of the multiple scattering. Starting from the expansion of the intensity logarithm in the functional Taylor series we formulate the general form of the DOAS equation. The thereby introduced variational derivative of the intensity logarithm with respect to the variation of the gaseous absorption coefficient, which is often referred to as the weighting function, is demonstrated to be closely related to the air mass factor. Employing some approximations we show that the general DOAS equation can be rewritten in the form of the weighting function (WFDOAS), the modified (MDOAS), and the standard DOAS equations. For each of these forms a specific equation for the air mass factor follows which, in general, is not suitable for other forms of the DOAS equation. Furthermore, the validity range of the standard DOAS equation is quantitatively investigated using a suggested criterion of a weak absorption. The results presented in this study are intended to provide a basis for a better understanding of the applicability range of different forms of the DOAS equation as well as of the relationship between the air mass factor and the weighting function. To facilitate the understanding of the paper content for unexperienced reader we start our discussion considering in detail the standard DOAS technique applied to the observations of the direct solar light transmitted through the Earth's atmosphere.
Highlights
The basic idea behind the usage of the Differential Optical Absorption Spectroscopy (DOAS) to detect atmospheric constituents can be traced back to Brewer et al (1973) and Noxon et al (1979), who have determined NO2 concentrations from the measurements of the transmitted solar light and zenith sky scattered light. Platt and Perner (1980) applied this technique for a long path measurements of tropospheric gases using an artificial light source
Employing some approximations we show that the general DOAS equation can be rewritten in the form of the weighting function (WFDOAS), the modified (MDOAS), and the standard DOAS equations
As can be seen on the right side of Eq (10) information about the amount of absorbing species can only be obtained if σλd (l) can not be approximated by a polynomial of the same order. It is worth noticing here, that Eq (10) can not be solved before the relationship between dl and dz is defined. This relationship is obvious for observations of the direct solar light transmitted through the atmosphere, we do not use it at this point to retain the generality of the standard DOAS technique
Summary
The basic idea behind the usage of the Differential Optical Absorption Spectroscopy (DOAS) to detect atmospheric constituents can be traced back to Brewer et al (1973) and Noxon et al (1979), who have determined NO2 concentrations from the measurements of the transmitted solar light and zenith sky scattered light. Platt and Perner (1980) applied this technique for a long path measurements of tropospheric gases using an artificial light source. The main goal of this paper is to derive several forms of the DOAS equation allowing for a significant contribution of multiple scattering processes and to demonstrate that for each form a distinct expression for the air mass factor follows This is done employing the general linear perturbation approach. Other recently published approaches to derive air mass factors (Slusser et al, 1996; Rozanov et al, 1998; Stammes and Koelemeijer, 1999; Marquard et al, 2000; Palmer et al, 2001) as well as their relationship to the presented forms of the DOAS equation and associated air mass factors are discussed in Sect. 12 we consider some example numerical simulations illustrating the performance of different DOAS equations being applied to the retrieval of ozone vertical columns from space-borne multispectral measurements of the scattered solar light in the UVvisible spectral range
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