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

and Physics cess Atmospheric Measurement Techniques Open Access Biogeosciences Open Access Atmos. Meas. Tech., 6, 1959–1980, 2013 www.atmos-meas-tech.net/6/1959/2013/ doi:10.5194/amt-6-1959-2013 © Author(s) 2013. CC Attribution 3.0 License. Open Access Regularisation model study for the least-squares retrieval of aerosol extinction time series from UV/VIS MAX-DOAS observations Climate for a of the Past ground layer profile parameterisation A. Hartl1 and M. O. Wenig2 2 Meteorological Institute, Ludwig-Maximilians-Universität München, Munich, Germany Correspondence to: A. Hartl () Earth System Dynamics Received: 6 February 2013 – Published in Atmos. Meas. Tech. Discuss.: 14 March 2013 Revised: 28 May 2013 – Accepted: 8 July 2013 – Published: 12 August 2013 Geoscientific Instrumentation Methods and boundary layer for a wide range of viewing directions and exDatatoSystems tinctions. It can thus be applied observational geometries Open Access scanning the sky in two angular dimensions and to retrieve further aerosol optical parameters in the boundary layer. Geoscientific Model Development 1 Introduction Open Access The experimental method to obtain tropospheric aerosol exHydrology and tinction and trace gas concentration profiles by applying Earthspectroscopy System (DOAS, Platt the differential optical absorption and Stutz, 2008) to ground-basedSciences observation of sun light intensities under different viewing directions has been an area of considerable activity in the past years – in field measurements in urban and remote areas (e.g. Wittrock et al., 2004; Irie et al., 2009; Lee et al., 2009; Li et al., 2010; Clémer Ocean Science et al., 2010; Frieß et al., 2011; Halla et al., 2011; Shaiganfar et al., 2011), within intensive measurement campaigns (e.g. Heckel et al., 2005; Sinreich et al., 2007; Brinksma et al., 2008; Roscoe et al., 2010; Irie et al., 2011; Vlemmix et al., 2011; Wagner et al., 2011; Zieger et al., 2011), as well as in comparative radiative model studies (Hendrick et al., Earth 2006; Wagner et al., 2007).Solid While the basic idea of this multi-axis DOAS, or MAX-DOAS, technique – namely to infer altitude information on an atmospheric absorber from its absorption signal along several light paths – is fairly straightforward, and the experimental setup relatively inexpensive, the actual conversion requires inversion of the unThe Cryosphere derlying radiative transfer equation. It strongly depends on tropospheric aerosol and, in general, the equation cannot be Open Access Open Access Open Access Published by Copernicus Publications on behalf of the European Geosciences Union. Open Access Abstract. The retrieval of tropospheric aerosol extinctions from MAX-DOAS observations of O4 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 underconstrained 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, singlescattering albedo and a Henyey–Greenstein phase function. Forward calculations are carried out online, i.e. without lookup 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 Open Access 1 School of Energy and Environment, City University of Hong Kong, Hong Kong, Hong Kong M 1960 linearised. Evolving in a series of studies (Wagner et al., 2002; Hönninger et al., 2004; Sinreich et al., 2005; Wagner et al., 2004; Frieß et al., 2006), it has therefore been suggested to fit forward-modelled absorption signals of an absorber with a known concentration profile, the oxygen dimer complex O4 , to the measured data in order to retrieve aerosol extinction profile parameters. This method has been used in several of the field measurements referred to above with different experimental setups and different retrieval procedures. Instruments, amongst other factors, may differ in the number of O4 wavelength absorptions bands their spectrometers cover and in the number and orientation of viewing angles under which their telescopes scan the sky. Apart from details of the DOAS fit itself – here the O4 absorption cross section is a source of uncertainty (Wagner et al., 2009; Clémer et al., 2010) – retrieval methods mainly differ in the way they parameterise the aerosol extinction and other aerosol parameters, in which radiative transfer model they use and in their fit algorithms. Currently there are mainly two kinds of approaches. One combines a linear parameterisation of the extinction profile by discrete layers and a statistical parameter estimation which in the area of satellite profile retrieval is commonly referred to as the optimal estimation method (Rodgers, 2000) to result in a non-linear least-squares problem. This approach bears the advantage of providing an estimate for the uncertainty of the retrieval, as well as diagnostic tools for the information content of the measurement. Frieß et al. (2006) employed this approach in their comprehensive model studies to show, among other things, that the retrieval improves with increasing number of O4 wavelength bands and if (relative) intensities are explicitly added to the fit quantities. Clémer et al. (2010) retrieved monthly aerosol extinction profiles in Beijing at four O4 wavelengths separately using this method. Both studies come to the conclusion that the number of extinction profile parameters constrained by a MAX-DOAS measurement is rather limited, and although the non-linearity of the problem makes it hard to give a generally valid number, it is even for ideal conditions somewhere below four. The second kind of approach may be characterised by making use of empirically motivated profile shapes such as linear or exponential functions (...truncated)