Abstract
Differential optical absorption spectroscopy (DOAS) is a powerful tool for detecting and quantifying trace gases in atmospheric chemistry [22]. DOAS spectra consist of a linear combination of complex multi-peak multi-scale structures. Most DOAS analysis routines in use today are based on least squares techniques, for example, the approach developed in the 1970s [18,19,20,21] uses polynomial fits to remove a slowly varying background (broad spectral structures in the data), and known reference spectra to retrieve the identity and concentrations of reference gases [23]. An open problem [22] is that fitting residuals for complex atmospheric mixtures often still exhibit structure that indicates the presence of unknown absorbers.   In this work, we develop a novel three step semi-blind source separation method. The first step uses a multi-resolution analysis called empirical mode decomposition (EMD) to remove the slow-varying and fast-varying components in the DOAS spectral data matrix ${\bf X}$. This has the advantage of avoiding user bias in fitting the slow varying signal. The second step decomposes the preprocessed data $\hat{{\bf X}}$ in the first step into a linear combination of the reference spectra plus a remainder, or $\hat{{\bf X}} = {\bf A}\,{\bf S} + {\bf R}$, where columns of matrix ${\bf A}$ are known reference spectra, and the matrix ${\bf S}$ contains the unknown non-negative coefficients that are proportional to concentration. The second step is realized by a convex minimization problem ${\bf S} = \mathrm{arg} \min \mathrm{norm}\,(\hat{{\bf X}} - {\bf A}\,{\bf S})$, where the norm is a hybrid $\ell_1/\ell_2$ norm (Huber estimator) that helps to maintain the non-negativity of ${\bf S}$. Non-negative coefficients are necessary in order for the derived proportional concentrations to make physical sense. The third step performs a blind independent component analysis of the remainder matrix ${\bf R}$ to extract remnant gas components. This step demonstrates the ability of the new fitting method to extract orthogonal components without the use of reference spectra.   We illustrate utility of the proposed method in processing a set of DOAS experimental data by a satisfactory blind extraction of an a-priori unknown trace gas (ozone) from the remainder matrix. Numerical results also show that the method can identify trace gases from the residuals.
Highlights
Trace gases play an important role in climate change and air quality of the Earth’s atmosphere
differential optical absorption spectroscopy (DOAS) is especially useful for measuring highly reactive species such as the free radicals OH, NO3, or BrO, and it provides a powerful tool for studying emissions, transformation and transport of chemicals throughout the troposphere and stratosphere
A typical experimental setup for a DOAS instrument consists of a continuous light source, e.g., a Xe-arc lamp, a light-absorbing sample, a grating spectrometer, and an optical detector
Summary
Trace gases play an important role in climate change and air quality of the Earth’s atmosphere. DOAS spectra contain overlapping absorption structures which consist of complex multiple scales and peaks They must be separated by the analysis routine to retrieve the concentrations of the trace gases. The existing DOAS approaches have two limitations: 1) the condition of least squares (that errors are normally distributed ) is often violated This suggests that a different norm other than l2 (least squares) norm should be used; 2) the fitting residuals for atmospheric samples are in most cases not pure noise due to imperfect references, atmospheric turbulence, instrument effects, and unknown trace gases. The new objective function for data fitting should overcome the limitations of least squares fitting, and help to maintain the non-negativity To tackle these problems, we have made an initial attempt of developing a semi-blind approach which contains three steps.
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