DOAS for flue gas monitoring—II. Deviations from the Beer-Lambert law for the U.V./visible absorption spectra of NO, NO 2, SO 2 and NH 3

Abstract

Deviations from the Beer-Lambert law were studied for the differential absorption cross-sections for NO, SO 2, NO 2 and NH 3. This was performed by simple calculations, computer simulations of spectra and by recordings of spectra for the above mentioned species at various total columns. The linearity studies for the DOAS instrument displayed large variations for the molecules studied and for different wavelength bands. In a calculation it was shown that the optical depth deviated from a linear concentration dependence by a term which was directly proportional to the statistical variance of the true absorption cross sections and proportional to the square of the total column, under the assumption of a boxcar instrument lineshape. Species exhibiting little variance or fine structure in their spectra, for instance NO 2, displayed a larger linear region compared with molecules exhibiting a rich structure, i.e., NO. The former species was linear to a total column of 3150 mg/m 2, which correspond to a maximum optical depth of 0.7, while the latter was linear to only 6 mg/m 2, corresponding to a maximum optical depth of 0.024, in the resolution range studied. The linear regions for the other species studied were 90 mg/m 2 for SO 2 at 230 nm, 180 mg/m 2 for SO 2 at 300 nm and 36 mg/m 2 for NH 3. The main effect of the nonlinearity was to cause a reduction in the peak height of the absorption. It was shown that the nonlinearity effect is independent on the spectral resolution when a large number of absorption lines are covered by the bandpass of the instrument. It was also shown that the largest change in linearity occurs when the resolution is similar in magnitude to the absorption linewidth. The nonlinear behavior for NO varied less than 2% in the temperature range 300–1000 K and the spectral resolution range 0.25–1 nm. The nonlinearity effect caused quantitative rather than qualitative changes of the spectral features and typical relative errors can be as high as 35% in a flue gas.