Wavelet covariance approach to measure convective boundary-layer structure

The convective boundary layer (CBL) plays a central role in moist convection and pollutant dispersion, yet its vertical structure remains difficult to diagnose objectively from radiosonde observations. Traditional approaches, often relying on single-variable gradients, emphasize identifying a single boundary-layer top, which can obscure the complexity of coupled thermodynamic transitions. To address this limitation, we extend the application of the Haar discrete wavelet transform (DWT) to simultaneously analyze vertical profiles of potential temperature (θ) and water vapor mixing ratio (r). This framework decomposes profiles into multiscale means and deviations, enabling diagnosis of multiple structural features, including surface-layer height, entrainment-zone depth and intensity, and boundary-layer height. By leveraging the localization properties of wavelets and explicitly quantifying θ–r covariance across scales, the method captures coupled transitions and reveals structural decoupling that may mask layer boundaries in traditional gradient-based approaches. Applications to high-resolution radiosonde data from the International H2O Project and the ARM Southern Great Plains Central Facility demonstrate that the method reliably identifies canonical CBL structures, while also objectively diagnosing atypical profiles characterized by diffuse gradients or θ–r decoupling. Sensitivity experiments further highlight the impact of vertical resolution, showing that coarse operational soundings smooth critical transitions and introduce systematic biases in diagnosed layer depths. These findings underscore the importance of scale-aware diagnostics for both research-grade and operational datasets. Overall, the enhanced Haar wavelet framework advances CBL analysis beyond single-height detection, providing a comprehensive, multiscale structural diagnosis that captures the complexity of thermodynamic coupling and entrainment processes. This approach offers a robust tool for improving understanding of boundary-layer dynamics and their role in atmospheric convection and pollutant transport.