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Turbulent Exchange Tensor in the Atmospheric Boundary Layer: An Inverse-Problem Approach Using Radiosonde Wind Observations with High Vertical Resolution
An inverse problem of reconstructing the turbulent exchange tensor from large archives of observed wind profiles within the Åkerblom–Ekman (A-E) model framework is investigated using high-vertical-resolution radiosonde observations. The reconstructed tensor provides improved agreement between modeled and observed wind profiles compared to classical formulations based on real turbulent exchange coefficient. Instead of the classical A-E model, where turbulent exchange is described by a single scalar coefficient, we introduce two independent functional degrees of freedom while preserving rotational invariance of the model in the horizontal plane. This generalization leads to a substantial reduction of model residuals. The observational archives are separated into cohorts according to season, time of day, latitude, boundary-layer height, surface roughness, the Richardson number, and the temperature difference at the boundary layer top and bottom. Such stratification further improves model performance and reveals systematic differences in the vertical structure of turbulent exchange under various atmospheric conditions. The lower boundary condition is optimized within a generalized third-type (Navier, Robin) formulation, replacing the classical no-slip condition. This also substantially improves the agreement between modeled and observed wind profiles in the near-surface layer.