| The elastic lidar equation is underdetermined and to solve it, a relationship must be derived between the backscatter and extinction coefficients. Several studies have either used a power law or linear relation, but none have compared the relative merits or errors of either approach. This study performs calculations to determine the best relation for stratus clouds and compares the results to previous studies. For typical cloud droplet size distributions, the backscatter and extinction cross-sections are computed from Mie theory. To determine the best relationship, three different types of fits are computed and then compared to previous studies. It is shown that a power law fit provides less error, but a linear fit is also applicable. Because each type of fit requires the determination of constants, a universal constant is computed and compared to the constants from other studies. Based on these findings, potential algorithms for determining size distributions are discussed. |
