The middle atmosphere, extending from the stratosphere to the lower thermosphere, functions as a critical transitional region between the lower and upper atmosphere. This layer exhibits complex dynamical processes—including gravity waves, atmospheric tides, and planetary waves—that substantially influence global circulation, energy transport, and vertical coupling across atmospheric layers. Precise characterization of these processes necessitates high-resolution temperature measurements, obtainable through Rayleigh scattering Lidar systems. These Lidars detect molecular backscatter signals, enabling accurate temperature profiling of the middle atmosphere with fine spatial and temporal resolution. Two principal methods are commonly employed to retrieve temperature profiles from Rayleigh Lidar measurements: the hydrostatic equilibrium method developed by Hauchecorne and Chanin (HC, also referred to as the C-H method), and the optimal estimation method (OEM). The HC method, a classical approach, utilizes hydrostatic equilibrium and integrates downward from a specified reference temperature at a high altitude. Although widely implemented, its accuracy depends significantly on the selected reference point. Conversely, OEM is a statistical retrieval method based on Bayesian theory. It integrates observational data with prior information to minimize uncertainties and enhance retrieval stability, proving particularly effective for nonlinear and ill-posed inverse problems. This study conducts a systematic comparison of the HC and OEM methods using both simulated and actual Lidar observations from Zhongshan Station, Antarctica. Their performance is assessed regarding retrieval accuracy, error propagation, and sensitivity to reference conditions, thus providing insights into Rayleigh Lidar retrieval method optimization.

Simulations were based on Rayleigh Lidar observations collected at Zhongshan Station on August 10, 2020. A synthetic Lidar signal was constructed using temperature profiles from the CIRA-86 model, which served as the true reference temperature. Temperature retrievals were then performed using both the HC and OEM methods. The HC method primarily relies on the hydrostatic equilibrium equation and the ideal gas law. An altitude was selected as the reference height where the uncertainty in the retrieved atmospheric density is 10%, and the corresponding model temperature at this altitude was used as the reference temperature. The OEM is based on Bayesian statistical theory and implemented using a least-squares optimization framework. Its fundamental principle involves the weighted integration of observational data and prior knowledge (such as the prior state vector and its covariance) in the error covariance space, thereby deriving the most physically reasonable state estimate that optimally fits the actual observations. In the application of the OEM, a suitable forward model [equation (14)] was constructed based on the Rayleigh Lidar equation, and the MSISE-00 model temperature was used as the a priori temperature profile.

Temperature retrievals using both HC and OEM methods were evaluated with the simulated lidar signals. The HC method, based on hydrostatic equilibrium, effectively retrieved the temperature structure across most of the vertical range when accurate reference temperatures were available (Fig. 2). However, the method exhibited high sensitivity to the chosen reference temperature, particularly within the 10?15 km region below the reference height where retrieval uncertainties increased substantially (Fig. 3). The OEM, evaluated through its averaging kernel matrix, demonstrated that observational data dominated the retrieval below 96 km (Fig. 5), while error budget analysis (Fig. 7) systematically quantified contributions from observation noise, forward model errors, and prior information. Additionally, the OEM’s enhanced robustness was confirmed through reference pressure perturbation tests (Fig. 8), demonstrating significant stability against such variations. Validation using actual Lidar measurements revealed good agreement between the two methods. Temperature differences remained generally below 2% below 87 km (Fig. 9), indicating consistency between the HC and OEM retrievals under well-constrained conditions.

In the present study, we compare HC and OEM temperature retrieval methods using Rayleigh Lidar signal from Zhongshan Station, Antarctica, and CIRA-86-based simulations. Key findings include: 1) both methods achieved accurate retrievals below 95 km with true reference parameters, with the HC method showing slightly better precision; 2) HC method exhibited strong sensitivity to reference temperature (especially within 10?15 km below the reference height), while OEM demonstrated superior robustness against reference pressure perturbations; 3) OEM enabled comprehensive uncertainty quantification (observation noise, model errors, etc.), offering distinct advantages for scientific analysis; 4) the HC method, due to its simplicity and low computational cost, remains well suited for operational or real-time applications. While both methods can reliably retrieve atmospheric temperature profiles, OEM is better suited for scientific applications requiring comprehensive uncertainty quantification, whereas the HC method is more applicable in scenarios prioritizing algorithmic simplicity and retrieval stability.