Uncertainties in the inversion problem depend also on the shape of the actual aerosol size distributions in the atmosphere. Our concern is that the Saharan dust size distributions have many large particles and the finite size range used in the inversions may lead to retrievals with a large particle tail considerably truncated. To see the influence of this limited size range, we proceed as follows. In Sect. 5.1 we computed the extinction coefficients from known aerosols size distribution. Now, starting from these extinction coefficients we do the inversion but with a size range limited from 20 to 3000 nm obtaining the corresponding aerosol size distributions and comparing them with the original ones. This "simulation'' have been done for desert models of Sect. 5.1 using the refractive index of 1.55 - 0.005i. The results were the following: 1) The retrieved volume size distribution consists of only one mode for the "desert with wind carrying dust'' model, masking the multimodal nature, coarse and dust modes, of the size distribution. 2) The retrieved volume size distribution for the "desert background'' model was accurate up to particles with a radius of 1000 nm. 3) For both size distributions, representing "desert with wind carrying dust'' and "desert background'', the retrieved volume was truncated for radii larger than 3000-4000 nm and the accumulation mode never appeared (it was absorbed by the coarse mode).
The uncertainties found in the simulation can be taken as the superior limit for the uncertainties in the retrieved size distribution at Teide Observatory of Fig. 9 (click here). Obviously, the dust load considered in the simulation models is much larger than the dust load measured at Teide Observatory. On the other hand, Saharan dust travels a long distance and the largest dust particles settle down before reaching the observatory. Therefore, only a small percentage of the largest dust particles will reach the observatory. For this reason, the retrievals show clearly two modes at Teide Observatory while only one mode appears in the simulation. This means that the coarse mode at Teide Observatory is not large enough to mask the accumulation mode as happened in the simulation. We conclude that the retrieved size distributions at Teide Observatory have smaller uncertainties than was found in the simulation. However, it is possible that the actual size distributions at Teide Observatory have the larger particle mode shifted to larger sizes. Considering the simulation result as an upper limit for the uncertainty, the maximum of the larger particle mode could be higher but not more than 25%, and the mode could be shifted 30% to larger sizes (maximum limit). The retrieved size distributions presented here can be consider as a model of Saharan and non-Saharan size distributions at Teide Observatory for calculating the extinction coefficients at different wavelengths in the interval from 450 nm to 870 nm with an uncertainty that depends on the error of the linear fits in Table 3 (click here). Also, they can be used to calculate aerosol optical properties that have little sensitivity to the uncertainties in the inversion method, for example, the asymmetry factor, which is an aerosol parameter needed in aerosol climate forcing calculations (Gonzalez Jorge & Ogren 1996).