  

Most of currently existing aerosol retrieval algorithms are aimed to determine the Aerosol Optical Thickness (AOT), i.e. columnar extinction by aerosol particles and their spectral behaviour. All higher level aerosol parameters (aerosol concentration, effective radius and others) can be derived from the magnitude and the spectral behaviour of the AOT. Thus, the spectral AOT may be regarded as the key parameter concerning retrieval of other aerosol properties. It is extracted by fitting modelled reflectance spectra to the measured reflectance spectra. This approach needs careful constraints based on the knowledge on molecular scattering, absorption and the surface reflectance (von HoyningenHuene et al. 2003). The first application to SCIAMACHY data is found in von HoyningenHuene et al. (2006). From UV wavelengths below 400 nm the Absorbing Aerosol Index (AAI) can be derived. The AAI indicates the presence of absorbing aerosol, mainly caused by strong events like Sahara dust outflows or biomass burning (see fig. 510). Initially developed as an error indicator for ozone retrieved from TOMS data (Herman et al. 1997), the AAI is the aerosol quantity with the longest data record. The AAI is derived as the residual between the measured reflectance from an atmosphere enriched with aerosols and the simulated reflectance of an atmosphere with only Rayleigh scattering, absorption by molecules, plus surface reflection and absorption (de Graaf and Stammes 2005). Such an algorithm using SCIAMACHY data at 340 nm and 380 nm delivers meaningful AAI values, in case properly calibrated spectra are used (de Graaf and Stammes 2005). 
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fig. 510:  Saharan desert dust outbreak to the Atlantic on July 25th, 2004. Shown are the SCIAMACHY AAI at 9:15 UTC of that day overlaid on a MODIS RGB picture, acquired around 11:10 UTC (right side of the plot) and 12:50 UTC (left side of the plot). High SCIAMACHY AAI values coincide with the dust plume, visible as a yellow haze on the MODIS image. (Image: M. de Graaf, KNMI)   

The combination of SCIAMACHY spectral information with data from high resolution images from AATSR on ENVISAT will enable the derivation of the aerosol type information, beside the AOT. The synergistic method SYNAER (HolzerPopp et al. 2002a, 2002b) can be applied toexploit SCIAMACHY together with AATSR to derive aerosol type information. 5.4 Profile Retrieval 5.4.1 Inversion Theory The forward modelling described earlier in chapter 5.1 is commonly employed to simulate a measured quantity, e.g., intensity of the radiation, for a predefined state of the atmosphere. Contrary to this, the objective of inversion problems is to retrieve certain characteristics of the atmospheric state – for example trace gas concentration profiles – based on the measured quantities. These can be for example the solar radiance transmitted through the Earth’s atmosphere in the occultation geometry or the radiance scattered by the Earth’s atmosphere or reflected by the surface in the limb or nadir geometry. The parameters to be retrieved from the measurements are represented by a model state vector x. For example, for trace gas vertical profile retrieval, the model state vector contains the number densities of atmospheric constituents defined at discrete altitude levels. 
Each state vector can be mapped to the measurement space by means of the forward model operator F to obtain the corresponding measurement vector y, i.e., for each atmospheric state described by vector x an appropriate measured quantity y can be simulated using a radiative transfer model as the forward model (see fig. 511).
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fig. 511: 
The principle of inversion for the retrieval of geophysical parameters. For further details see the text. (Graphics: IUPIFE, University of Bremen) 

In the case of SCIAMACHY occultation or limb measurements, the measured quantities are represented by a set of intensities measured at different tangent heights in selected spectral windows. Taking into account that measurements are made to a finite accuracy, a measurement errore has to be considered which is commonly assumed to be normally distributed with mean zero and known error covariance matrix Sy. Thus, the relationship between the model state vector and the measurement vector can be written as (equ. 57)
In order to solve the inverse problem, this nonlinear relationship in equ. 57 has to be linearised expanding the forward model operator, F, as a Taylor series about a guessed value x0 of the solution. Ignoring the higherorder terms one obtains (equ. 58)
Here, K0 is the linearised forward model operator. In the discrete representation the linearised forward model operator is given by the weighting function matrix describing the sensitivity of the measured quantities to the variation of the atmospheric parameters at different altitude levels. This weighting function matrix is calculated with the radiative transfer model.
Atmospheric inversion problems are commonly ‘illposed’. Thus, additional constraints need to be introduced to determine a geophysical solution from the set of mathematically allowed solutions. Most commonly, the methods of statistical regularisation, as described e.g. by Rodgers (2000) are applied, i.e., the maximum likelihood condition, a priori value of the solution, x0, and its covariance matrix, Sa, are employed to solve the inversion problem. In this case the solution is found by minimising the following quadratic form (equ. 59)