A Physically-Guided and Stage-Wise Machine Learning Framework for Mixing Layer Height Retrieval Based on Doppler Lidar Observations

Continuous and accurate retrieval of mixing-layer height (MLH) is essential for understanding convective boundary-layer (CBL) dynamics, air quality forecasting, and land–atmosphere interactions. Traditional machine learning methods often treat the CBL as a single regime, neglecting key physical constraints such as its strong diurnal evolution and thus incurring significant forecast errors. This study introduces a physically informed, stage-dependent framework that integrates high-resolution Doppler lidar observations with regime-specific thermodynamic and dynamical constraints. The CBL diurnal cycle is segmented into four distinct stages — Initiation, Growth, Peak, and Decay — using local-time thresholds informed by key physical drivers derived from multisource observations (e.g., heat fluxes, turbulent kinetic energy, lower tropospheric stability). A sequential prediction approach uses prior states to ensure temporal consistency, integrating the four stage-specific models into a seamless framework for capturing the full diurnal MLH evolution. Evaluated at the ARM Southern Great Plains C1 site, the framework achieves R² = 0.88 and MAE = 0.18 km, with reasonable near-site transferability at the nearby E37 and E39 sites within the same climatic regime (R² = 0.83–0.86). SHAP analysis reveals stage-dependent physical drivers: mechanical turbulence dominates Initiation; cumulative heating controls Growth; entrainment prevails during Peak; and radiative processes govern Decay. Stage-dependent driver variations are shown to outweigh seasonal shifts, and ablation studies confirm that incorporating physical constraints contributes more to performance gains than algorithmic tuning alone. This physics-guided machine learning framework offers a valuable tool for ground-based profiling networks.