Wavelet covariance approach to measure convective boundary‐layer structure

The convective boundary layer (CBL) strongly influences moist convection and pollutant dispersion, yet objective diagnosis of its vertical structure from radiosondes remains challenging. Although Haar wavelet transforms have been employed to analyze CBL structure, most studies emphasize identifying a single boundary‐layer top, typically inferred from a one‐variable profile. We extend the application of the Haar discrete wavelet transform (DWT) to simultaneously analyze vertical profiles of potential temperature () and water vapor mixing ratio ( r ). Rather than focusing solely on CBL height, the method decomposes profiles into multiscale means and deviations to diagnose multiple structural features, including surface‐layer height, entrainment zone depth and intensity, and boundary‐layer height. By leveraging wavelet localization and explicitly quantifying θ – r covariance across scales, the framework captures coupled thermodynamic transitions and reveals structural decoupling that may obscure layer boundaries in traditional gradient‐based approaches. Applications to high‐resolution radio sounding data from the International H 2 O Project and the ARM Southern Great Plains Central Facility demonstrate that the method reliably captures canonical CBL structures, while objectively identifying atypical profiles characterized by diffuse gradients or – r decoupling. Sensitivity experiments on vertical resolution further reveal how coarse operational soundings smooth critical transitions and introduce systematic biases in diagnosed layer depths. Overall, this enhanced Haar wavelet framework advances CBL analysis from single‐height detection toward comprehensive, scale‐dependent structural diagnosis applicable to both research‐grade and operational datasets.