Evaluation of a Method for Calculating the Height of the Stable Boundary Layer Based on Wind Profile Lidar and Turbulent Fluxes

The height of the stable boundary layer (SBL), known as the nocturnal boundary layer height, is controlled by numerous factors of different natures. The SBL height defines the state of atmospheric turbulence and describes the diffusion capacity of the atmosphere. Therefore, it is unsurprising that many alternative (sometimes contradictory) formulations for the SBL height have been proposed to date, and no consensus has been achieved. In our study, we propose an iterative algorithm to determine the SBL height $h$ based on the flux–profile relationship using wind profiles and turbulent fluxes. This iterative algorithm can obtain temporally continuous, accurate estimates of h and is widely applicable. The predicted $h$ presents relatively good agreement with four observation-derived SBL heights, $h_J$, $h_1$, $h_i$, and $h_{\theta }$ ($h_J$: maximum wind speed height, $h_1$: zero wind shear height, $h_i$: temperature inversion height, and $h_{\theta }$: height at which 0.8 times the inversion strength appears for the first time), especially with $h_{\theta }$, which shows the best fit. In addition, $h$ exhibits a low absolute difference and relative difference with $h_J$, which presents the second-best result. The agreement with $h_i$ and $h_1$ may be satisfactory, but small differences are observed, and the one standard deviation of the mean relative difference is large. In addition, the predicted h is compared with other SBL height estimation methods, including diagnostic, ${\lambda }_1$, ${\lambda }_2$ and ${\lambda }_3$ (three typical dimensional scale height parameters) and prognostic equation-based methods, $\lambda \left(h\right)$ (an equation for the growth of $h$ developed). The diagnostic formulas are found to be appropriate, especially under extremely stable conditions. Additionally, the equation of ${\lambda }_3$ presents the best result of all the dimensional scale height parameters. However, the prognostic equation $\lambda \left(h\right)$ in our study is very unsatisfactory.