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The SASKMART algorithm applies a Multiplicative Algebraic Reconstruction Technique coupled with the Sasktran V2  radiative transfer forward model to invert the OSIRIS line of sight radiances and produce height profiles of ozone and aerosols.  The OSIRIS line-of-sight radiances typically scan from 7 km to 80 km altitude at approximately 2 km intervals with ~1 km height resolution although the presence of tropospheric cloud raises the lowest useful altitude.

The MART algorithm combines ratios of the measured radiances at specific wavelengths and altitudes to produce a set of retrieval vectors (\(y_{kj}\)) which are the entities used by the algorithm to derive the desired height profiles (\(x_{i,k}\)). The choice of retrieval vectors is an important part of the algorithm. They have been selected so they are almost always positive throughout the fitting region, a condition which helps the algorithm avoid the undesirable oscillations common in many other techniques.  The O3 section defines 8 retrieval vectors using 11 wavelengths providing good sensitivity across the entire altitude range.  The aerosol section defines 1 retrieval vector. The retrieval vector definitions also bestows the algorithm with almost no sensitivity to errors in instrument absolute calibration.

The MART algorithm iteratively converges the selected height profile using a mulitplicative correction factor for each iteration

$$x^{n+1}_i = \alpha_{i}x^{n}_i$$


$$\alpha_{i} = \sum_k \alpha_{ik}W_{ki}$$


$$\alpha_{ik}=\sum_{j}\left( \frac{y_{kj}^{obs}}{y_{kj}^{mod}}W_{ji}\right)$$