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With the increased installation of wind farm in complex terrain, the wake expansion of large-scale wind turbine under real conditions downstream a hill is an elusive target and one of the main challenges in the optimization of the layout, operation, and control of wind farm. However, previous studies based on CFD simulations and typical commercial software have controversial descriptions about the wake expansion downstream a hill (Wei et al., 2021) [1]. Research of this paper focus on the velocity deficits detections in real complex wind farm conditions though LiDAR-based observation with an analytical wake model been proposed and validated which can describe the velocity distributions down of a turbine on the top of a real hill. The previous three-dimensional Jensen-Gaussian (3DJG) wake model of our team is improved with the Coanda effect (wall attachment effect) been considered. The altitude sink, Δ h of wind turbine is substituted into the new wake model. In addition, the wind shear effect is also considered, and the wake expansion rate k is modified in the new model. Two types of Doppler LiDARs, WindMast WP350 and Wind3D 6000, were used to measure the inflow wind profile and the wake expansion in the three-dimensional (3D) space downstream two wind turbines on the top of a hill in one complex wind farm in northern Hebei Province, China. The accuracy of the improved 3DJG wake model is compared with the field measured data and other typical wake models. Results show that the improved 3DJG wake model performance better in sank wake descriptions in both horizontal and vertical plane for wake in wind turbine on the top of a hill. The proposed model and observed wake expansion data in real conditions in this paper can provide theoretical and data support for wind farm micro-siting, the downstream turbine's control strategy adjustment as well as wind power prediction of for wind turbine on the top of a hill. • An improved 3DJG wake model for turbines on the top of a hill is proposed. • Conada effects is considered in the derivation of the model. • Wake and terrain superposition method of 'D-line' succeeds in field-measured. • The actual wind farm data measured by LiDAR are used to verify wake model. • Performance of 3DJG is better on wake prediction considering the wake sinking. [ABSTRACT FROM AUTHOR]