Notes on Temperature-Dependent Lidar Equations

The temperature dependence of molecular backscatter coefficients must be taken into account when narrowband interference filters are used in lidar measurements. Thus, the spectral backscatter differential cross section of the molecules involved in the backscattering of the radiation has to be calculated or measured and the interference filter transmission efficiency must be known. The present paper is intended to describe in an easily reproducible manner the procedure involved in calculating the temperature-dependent functions introduced in the lidar equations, including the computation of the differential cross sections for air, nitrogen, and water vapor. The temperature-dependent functions are computed for the Howard University Raman lidar (HURL). The interference filter efficiencies are given by the manufacturer. Error estimates in water vapor mixing ratio and aerosol backscatter ratio involved when temperature-dependent functions are omitted are given for measurements taken with HURL. For the data analyzed, it is found that errors in estimating the water vapor mixing ratio are up to similar to 6% while in estimating the aerosol backscattering ratio the errors are up to similar to 1.3% in the planetary boundary layer and similar to 2.2% in cirrus clouds. Theoretical computations are performed to determine temperature-dependent functions for nitrogen, water vapor, and their ratio, using simulated Gaussian-shaped filters. The goal is to find the optimum combination of different filters that will determine the ratio profiles of the temperature-dependent functions that are either the closest to unity or the least variable. The analyses reveal that quite constant profiles can be obtained for several combinations of the filters.