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The retrieval of tropospheric aerosol extinctions from MAX-DOAS observations of O<sub>4</sub> using a small number of three or four extinction profile parameters suitable for boundary layer reconstruction is investigated with respect to the following questions. First, to what extent does this nominally over-constrained pure least-squares problem for the inversion of the radiative transfer equation require regularisation and how should parameters of the regularisation be chosen? Second, how can a lack of information in the under-constrained case be best compensated by using the information contained in a sequence of observations and by explicitly including intensities into the fit?    The forward model parameterises the optical properties of the boundary layer aerosol by its extinction profile, single-scattering albedo and a Henyey–Greenstein phase function. Forward calculations are carried out online, i.e. without look-up tables. The retrieval uses a Tikhonov regularisation combined with an approximate L-curve criterion and empirical a priori information from the retrieval sequence based on previous valid solutions. The consistency of the approach is demonstrated in selected model case studies assuming a polluted urban scenario and westward viewing direction of the instrument. It is shown that a dynamic choice of the regularisation parameter is crucial for high aerosol load and large diurnal variations. The quality of the retrieval can be improved significantly if the retrieval sequence and thus the a priori is chosen according to the information content of the measurement series. Additional intensities improve the solution for all solar angles if suitably weighted. This flexible retrieval algorithm allows for reconstruction of aerosol profiles in the boundary layer for a wide range of viewing directions and extinctions. It can thus be applied to observational geometries scanning the sky in two angular dimensions and to retrieve further aerosol optical parameters in the boundary layer

atmospheric measurement techniques

Regularisation model study for the least-squares retrieval of aerosol extinction time series from UV/VIS MAX-DOAS observations for a ground layer profile parameterisation