Uncertainty Evaluation of Atmospheric Temperature Retrieval Using Rayleigh Lidar Based on the Optimal Estimation Method

As a new retrieval method, the Optimal Estimation Method (OEM) is playing an increasingly important role in detecting the atmospheric environment by lidar. In this study, the necessity of calculating the uncertainty of retrieval results was analyzed first. To characterize the reliability of the atmospheric temperature inversion results by lidar, the OEM uncertainty formula was derived and the sources of uncertainty was clarified. There were four sources of uncertainty, which were smoothing uncertainty, model parameter uncertainty, forward model uncertainty and noise uncertainty. Regarding the problem of using Rayleigh lidar to retrieve the temperature of the middle atmosphere, the forward model was derived based on the lidar equation, ideal gas state equation, and hydrostatic equilibrium as reasonable assumptions. Based on the simulated echo photon profiles of the Rayleigh lidar calculated by forward model, the middle atmospheric temperature and the corresponding uncertainty was calculated, which demonstrated that the main uncertainty sources in the OEM retrieval process are the reference pressure uncertainty and noise uncertainty. Using the Monte Carlo method (MCM), the OEM uncertainty verification framework was established and the uncertainty values generated by different sources of uncertainty were verified. Afterwards, the total uncertainty value caused by all sources of uncertainty was also verified. Results showed that the uncertainty calculated by two different methods and the total uncertainty were consistent below the altitude of 85 km, proving the accuracy of the OEM uncertainty theories. In addition, temperature retrieval based on measured results by Rayleigh lidar was performed. The characteristics of the measured data were introduced in detail, and the retrieval results and corresponding uncertainties were calculated. The results prove the conclusion that the main uncertainty sources in the OEM inversion process are the reference pressure uncertainty and noise uncertainty. The work of this article paves the way for the applications of lidar in monitoring the atmospheric environment.