## 1 Introduction  
The mixed layer (ML), also known as the convective boundary layer, is the lower part of the atmospheric boundary layer (ABL) which is directly influenced by the Earth's surface and responds to surface forcing with a timescale of about an hour [1]. Mixed layer height (MLH) is defined as the height of ML top. Below the ML top, the heat, moisture, pollutants, and small gas constituents are mixed in the vertical. Therefore, the MLH is one of the key parameters in the boundary layer parameterization of weather and air quality models [2, 3]. In particular, the marine ML is important to marine low cloud process and material exchange between the ocean and low atmosphere; thus, the marine MLH is critical to successful climate simulation [4] and accurate air-sea surface flux parameterization [5].  
The material mixing in the ML is driven by convective turbulence; thus, the MLH can be retrieved from turbulence intensity, which is usually characterized by the vertical wind velocity variance or turbulent kinetic energy dissipation rate (TKEDR). To retrieve the MLH, the turbulence intensity should first be estimated. Numerous instruments have been used for turbulence intensity estimations. Traditionally, an in situ technique measures the point-wise data using radiosondes mounted on balloons [6]. Recently, a remote-sensing technique is developed to measure the data profile from the ground to stratosphere using sodars, radars, or lidars [7, 8]. Among these, coherent Doppler wind lidar (CDWL) is one of the most promising instruments thanks to its high precision, high range resolution, and strong immunity to electromagnetic interference [9, 10, 11, 12, 13, 14, 15].  
The turbulence intensity estimated by the CDWL can be used as a tracer to retrieve MLH because there is usually a decrease in turbulence intensity profile at the ML top [16]. Based on this characteristic, a threshold method with rapidity and low uncertainty is developed. For an appropriate threshold of vertical wind velocity variance which represents the vertical component of turbulence kinetic energy, the variance is larger than the threshold below the MLH and vice versa. Note that the value of variance threshold varies from different locations. For example, the optimum variance thresholds in Hefei and Bejing, China are 0.06 and 0.1 m\({}^{2}\) s\({}^{-2}\), respectively [11, 17]. The value is found to vary with convective turbulence intensity. A larger value of 0.3 m\({}^{2}\) s\({}^{-2}\) is optimum for a strong convective boundary layer over a tropical rain forest, while a smaller value of 0.04 m\({}^{2}\) s\({}^{-2}\) is optimum for a marine boundary layer due to its weak convection [18, 19].  
As an attractive alternative, the MLH is also able to be retrieved by setting an appropriate TKEDR threshold because TKEDR represents the conversion of turbulent kinetic energy to heat. For the TKEDR estimated by structure function algorithm, the optimum threshold at inland site has been determined as 10\({}^{-4}\) m\({}^{2}\) s\({}^{-3}\) in Siberia, Russia [20]. It is worth noting that the value of TKEDR threshold at the marine site has not been investigated.  
In this work, to investigate the applicability of the inland optimum TKEDR threshold in retrieving marine MLH, ground-based experiments are conducted at both inland and marine sites. After that, a ship-borne experiment is carried out to realize marine MLH detection. If not specified, LST (local standard time, LST = UTC + 8) is used.