Linearisation of the effects of spectral shift and stretch in DOAS analysis

Differential Optical Absorption Spectroscopy (DOAS) is a widely used method to quantify atmospheric trace gases from spectroscopic measurements. While DOAS can, in principal, be described by a linear equation system, usually nonlinearities occur, in particular as a consequence of spectral misalignments. Here we propose to linearise the effects of a spectral shift by including a "shift spectrum", which is the first term of a Taylor expansion, as pseudo-absorber in the DOAS fit. The effects of a spectral stretch are considered as additional wavelength-dependent shifts. Solving the DOAS equation system linearly has several advantages: the solution is unique, the algorithm is robust, and it is very fast. The latter might be particularly important for measurements with high data rates, like for upcoming satellite missions.