Differential optical absorption spectroscopy (DOAS) and air mass factor concept for a multiply scattering vertically inhomogeneous medium: theoretical consideration

摘要

The Differential Optical Absorption Spectroscopy (DOAS) techniqueis widely used to retrieve amounts of atmospheric species frommeasurements of the direct solar light transmitted through the Earth'satmosphere as well as of the solar light scattered in the atmosphere orreflected from the Earth's surface. For the transmitteddirect solar light the theoretical basis of theDOAS technique represented by theBeer-Lambert law is well studied. In contrast, scarcely investigated isthe theoretical basis and validity range of the DOAS method for those caseswhere the contribution of the multiple scattering processes is notnegligible. Our study is intended to fill this gap by means of a theoreticalinvestigation of the applicability of the DOAS technique for the retrieval ofamounts of atmospheric species from observations of the scattered solar lightwith a non-negligible contribution of the multiple scattering.Starting from the expansion of the intensity logarithm in the functionalTaylor series we formulate the general form of the DOAS equation.The thereby introduced variational derivative of the intensitylogarithm with respect to the variation of the gaseous absorption coefficient,which is often referred to as the weighting function, is demonstrated to beclosely related to the air mass factor.Employing some approximationswe show that the general DOAS equation can be rewritten in the form ofthe weighting function (WFDOAS), the modified (MDOAS), and thestandard DOAS equations. For each of these forms a specificequation for the air mass factor follows which, in general, is notsuitable for other forms of the DOAS equation. Furthermore,the validity range ofthe standard DOAS equation is quantitatively investigated using a suggestedcriterion of a weak absorption.The results presented in this study are intended to provide a basis for abetter understanding of the applicability range of different forms of theDOAS equation as well as of the relationship between the air mass factorand the weighting function. To facilitate the understanding of the papercontent for unexperienced reader we start our discussion consideringin detail the standard DOAS technique applied to the observationsof the direct solar light transmitted through the Earth's atmosphere.