Simple Monte Carlo methods to estimate the spectra evaluation error in differential-optical-absorption spectroscopy

Differential-optical-absorption spectroscopy (DOAS) permits the sensitive m easurement of concentrations of trace gases in the atmosphere. DOAS is a te chnique of well-defined accuracy; however, the calculation of a statistical ly sound measurement precision is still an unsolved problem. Usually one ev aluates DOAS spectra by performing least-squares fits of reference absorpti on spectra to the measured atmospheric absorption spectra. Inasmuch as the absorbance from atmospheric trace gases is usually very weak, with optical densities in the range from 10(-5) to 10(-3), interference caused by the oc currence of nonreproducible spectral artifacts often determines the detecti on Limit and the measurement precision. These spectral artifacts bias the l east-squares fitting result in two respects. First, spectral artifacts to s ome extent are falsely interpreted as real absorption, and second, spectral artifacts add nonstatistical noise to spectral residuals, which results in a significant misestimation of the least-squares fitting error. We introdu ce two new approaches to investigate the evaluation errors of DOAS spectra accurately. The first method, residual inspection by cyclic displacement, e stimates the effect of false interpretation of the artifact structures. The second method applies a statistical bootstrap algorithm to estimate proper ly the error of fitting, even in cases when the condition of random and ind ependent scatter of the residual signal is not fulfilled. Evaluation of sim ulated atmospheric measurement spectra shows that a combination of the resu lts of both methods yields a good estimate of the spectra evaluation error to within an uncertainty of similar to 10%. (C) 1999 Optical Society of Ame rica.