I work as an air quality researcher and am trying to calculate two unknowns in an equation. I have a set of results (ATN= attenuation of light measured on a filter; BC= black carbon concentration) and according to literature the data should fit the following equation (derived from the Lambert-Beer-law):
ATN= -100 ln (α + (1-α) exp(-σ [BC])).
1) I have a set of ATN and corresponding BC measurements (about 300) but need to determine best fit for α (a sort of filter constant) and σ (specific attenuation) as these vary according to the measurement site and filter used.
2) I have a further 600 measurement where I only have attenuation and need to then use the equation and calculate BC.
What's the best way to go about it/best software to use maybe and how to use it (for problem number one)? And for step two I might need some help solving the equation to BC as well...