Similar to issue #50 The Lidar constant calculations are currently using the wrong molecular backscatter for the calculations of the inelastic wavelengths.
The LC for the inelastic wavelengths (387 and 607) are currently calculated from following equation in an area not affected by the overlap function ei. $O^{Ra}(R) = 1$
$$ C^{Ra}_{sys}(R) = \frac{R^2 P^{Ra}(R)}{ O^{Ra}(R) \beta^{el}_{mol}(R) exp\Big( - \int^{R}_{0} \big[ \alpha^{el}_{aer}(r) + \alpha^{el}_{mol}(r) + \alpha^{Ra}_{aer}(r) + \alpha^{Ra}_{mol}(r) \big] dr \Big)} $$
However, the inelastic / Raman LCs should be calculated from this equation:
$$ C^{Ra}_{sys}(R) = \frac{R^2 P^{Ra}(R)}{ O^{Ra}(R) \beta^{Ra}_{mol}(R) exp\Big( - \int^{R}_{0} \big[ \alpha^{el}_{aer}(r) + \alpha^{el}_{mol}(r) + \alpha^{Ra}_{aer}(r) + \alpha^{Ra}_{mol}(r) \big] dr \Big)} $$
Where the molecular backscatter of the inelastic wavelength is used instead of the one for the elastic wavelength.
Additionally, whether the actual retrieved extinction or the extinction approximated by $\beta_{aer} \times LR$ is used when calculating the LC do affect the final LC. This is especially clear at the top of aerosol layers. Currently in PicassoPy only the retrieved extinction is used while in Picasso the retrieved extinction is used for the Klett retrieved LC and the approximation is used for the Raman retrieved LC. As both methods seems to have their upsides and downsides depending on the situation, I propose that a new config variable is added flagUseRetrievedExt4LCClac to let the user define which extinction to use in the LC calculations. Now the question is, do we want to use the same (user defined) methodology for the extinction used for both Klett and Raman retrieved LCs or do we want to use different methodologies like in Picasso?
Similar to issue #50 The Lidar constant calculations are currently using the wrong molecular backscatter for the calculations of the inelastic wavelengths.
The LC for the inelastic wavelengths (387 and 607) are currently calculated from following equation in an area not affected by the overlap function ei.$O^{Ra}(R) = 1$
However, the inelastic / Raman LCs should be calculated from this equation:
Where the molecular backscatter of the inelastic wavelength is used instead of the one for the elastic wavelength.
Additionally, whether the actual retrieved extinction or the extinction approximated by$\beta_{aer} \times LR$ is used when calculating the LC do affect the final LC. This is especially clear at the top of aerosol layers. Currently in PicassoPy only the retrieved extinction is used while in Picasso the retrieved extinction is used for the Klett retrieved LC and the approximation is used for the Raman retrieved LC. As both methods seems to have their upsides and downsides depending on the situation, I propose that a new config variable is added
flagUseRetrievedExt4LCClacto let the user define which extinction to use in the LC calculations. Now the question is, do we want to use the same (user defined) methodology for the extinction used for both Klett and Raman retrieved LCs or do we want to use different methodologies like in Picasso?