## 3 Determination of TKEDR Threshold for Retrieving MLH  
The MLH can be retrieved from both the aerosol concentration and turbulence intensity. The MLH retrieval results based on aerosol and turbulence are coincident at noon [23]; thus, the MLH retrieval result based on aerosol at noon can be used as a reference to determine the turbulence intensity threshold for retrieving MLH.  
The CNR, which is a measure of aerosol backscattered signal, represents aerosol concentration. There is usually a sharp decrease in CNR profile at the ML top because the aerosol concentration in the ML is much higher than that in the free atmosphere. Here, the Haar wavelet covariance transform (HWCT) of CNR is calculated to locate the MLH. The Haar function is defined as [24]:  
\[h\left(\frac{z-b}{a}\right)=\left\{\begin{array}{c}+1,\ b-a/2\leq z\leq b\\ -1,b\leq z\leq b+a/2\\ 0,\text{\emph{elsewhere}}\end{array}\right. \tag{1}\]  
where \(z\) is height, \(a\) is function dilation, and \(b\) is center position. The covariance transform of the function is defined as:  
\[W_{f}(a,b)=\frac{1}{a}\int_{z_{b}}^{z_{t}}\!f(z)h\left(\frac{z-b}{a}\right)\!dz \tag{2}\]  
where \(f(z)\) is range-corrected CNR, and \(z_{b}\) and \(z_{t}\) are the bottom height and top height of selected range. For a given dilation \(a\), the height of the maximum of local maximums in \(W_{f}(a,b)\) is the MLH. Moreover, at a well-mixed layer top, there is an entrainment zone where materials are not fully mixed, resulting in a decrease in turbulence intensity. Since the turbulence intensity can be characterized by TKEDR, the MLH is also able to be located via setting an appropriate TKEDR threshold.  
Figure 1(a)-1(d) show the determination process of TKEDR threshold in Inner Mongolia. Figure 1(a)-1(e) show CNR-related profiles at noon, including CNR measured by CDWL, normalized range-corrected CNR and its HWCT. Figure 1(d) shows the TKEDR profile measured by CDWL at the same time. To locate the MLH, the CNR is multiplied by the square of range and normalized in a selected range of 0-5 km to obtain the normalized range-corrected CNR at first. Then, its HWCT is calculated according to Equation (2) with a dilation of 250 m. As seen in the blue-shaded area in Figure 1(b), there is a sharp decrease in the range-corrected CNR profile. As the range-corrected CNR decreases, its HWCT increases rapidly, resulting in a local maximum. The local maximum height signed by a blue dotted line in Figure 1(c) is the MLH. Finally, an MLH\({}_{\text{CNR}}\) of 2.65 km is obtained, which is denoted by a blue circle.  
Here, the MLH\({}_{\text{CNR}}\) is used to determine the value of the TKEDR threshold. Since Inner Mongolia is an inland site, the inland optimum TKEDR threshold of \(10^{-4}\) m\({}^{2}\) s\({}^{-3}\) is preset and signed by a pink dotted line in Figure 1(d). As a result, an MLH\({}_{\text{TKEDR}}\) of 2.68 km is obtained and denoted by a pink circle. One can see that the MLH\({}_{\text{TKEDR}}\) agrees well with the MLH\({}_{\text{CNR}}\); thus, the threshold preset here is appropriate. Figure 1(e)-1(h) show the threshold determination at the other inland site (Hefei). The threshold of \(10^{-4}\) m\({}^{2}\) s\({}^{-3}\) is still appropriate because the obtained MLH\({}_{\text{TKEDR}}\) of 1.64 km agrees well with the MLH\({}_{\text{CNR}}\) of 1.61 km. In particular, the threshold determination at the marine site (Sansha) is shown in Figure 1(i)-1. Since the MLH\({}_{\text{CNR}}\) is 0.78 km, the MLH\({}_{\text{TKEDR}}\) is preset as 0.78 km. As aresult, the threshold of \(10^{-4}\) m\({}^{2}\) s\({}^{-3}\) is determined. The results indicate that the inland optimum TKEDR threshold is applicable in retrieving marine MLH.