| [3] — |  |
In this formulation, we have the j absorber slant column densities as unknowns and in addition the contributions from Mie and Rayleigh scattering. As discussed in section xxx, both Mie and Rayleigh scattering cross-sections have a wavelength dependency that can be expressed by a polynomial:
| [4] — |  |
Because the only quantities of interest are the SCj, the scattering parts can be approximated by a polynomial of low order (p <= 4):
| [5] — |  |
and by inserting this into the equation we obtain
| [6] — |  |
A complication that arises from the use of a polynomial to account for scattering as the part of the absorption which changes slowly with wavelength will also be taken up by this term. Therefore, the absorption cross-sections σ have been replaced by the differential absorption cross-sections σ', which are the high pass filtered parts of the absorption cross-sections as illustrated in the figure. This separation into high frequency and low frequency parts of the signal is the 'differential' part of DOAS. This process can be represented graphically as follows:
Fig : Absorption cross-section and scattering polynomial.
Image: AT2-ELS