RamBackscattering, extinction, and liquid water content in fog: a detailed study of their relations for use in lidar systems

A solution to the single-scattering lidar equation to infer optical extinction, liquid water content W, and visibility in a fog through a monostatic pulsed lidar, requires the use of the relations, and combinations of them, between backscattering coefficient beta, extinction coefficient sigma, and W. To this end, beta and sigma have been computed for 239 droplet size spectra and forty wavelengths from 0.25 to 12 microm, together with W, and the three relations beta vs sigma, W vs sigma and sigma(0.55 microm) vs sigma have been determined. The analysis of their behavior with wavelength shows that (1) the relation beta vs sigma is mostly reliable in the lambda = 0. 25-2-microm region, where the dispersion of the beta values around the best-fit curve is within 20%; (2) the relation W vs sigma is generally not well verified (the dispersion is centered around 30%), and when used in connection with the beta vs sigma relation to infer liquid water content, their joint dispersion P(D) is always greater than 20%; (3) the relation sigma(0.55 microm) vs sigma is well verified in the region lambda = 0.25-2 microm (dispersion within 15%), and when used in connection with the beta vs sigma relation to infer visibility P(D) appears to be minimum at lambda congruent with 0.35 microm (P(D) = 4.7%).