Physics-Informed Neural Networks for Multi-Location ABL Wind Profiling with Minimal Instrumentation

The vertical wind profile within the Atmospheric Boundary Layer (ABL) is a critical variable for a wide range of applications, including wind energy, air traffic and Unmanned Aerial System (UAS) management, pollutant dispersion, and urban air mobility. However, its accurate characterization typically requires expensive vertical-profiling LiDAR instruments, which limits the number of locations that can be simultaneously monitored. Building upon previous work in which machine-learning algorithms were trained on LiDAR data from the University of León (Spain) to reconstruct full ABL wind profiles from a single near-surface measurement, this study replaces the traditional data-driven neural network approach with Physics-Informed Neural Networks (PINNs), embedding a physical constraint directly into the loss function as evaluated by automatic differentiation, and tests two such constraints under architectural control: the Ekman boundary-layer momentum balance, closed with a Monin–Obukhov eddy viscosity, and a shear-constrained formulation based on a power-law profile with an inferred exponent. With dense supervision at the target heights, neither constraint improves on an architecture-matched network without a physical term (RMSE 1.35–1.36 m/s, direction MAE 20.1–20.4∘ across all three, Kruskal–Wallis p=0.0125). In a vertical-extrapolation protocol, training with gates up to 111 m, selecting models by their skill at 140 m, and testing blind on 170–300 m, the Ekman constraint shows no detectable advantage over its own architectural control. In contrast, the shear-constrained model does, reaching 1.80±0.01 m/s speed RMSE and 27.0∘±0.3∘ direction MAE against 2.66±0.10 m/s and 34.2∘±1.8∘ for the Ekman-constrained arm and 2.61±0.12 m/s and 33.9∘±2.0∘ for the physics-free arm, which are statistically indistinguishable from one another; the shear-constrained gain is confirmed against its own architectural control (2.64±0.08 m/s, 33.0∘±1.8∘, matching the physics-free arm), ruling out the additional output as the explanation, and converts an erratic extrapolator into a stable one. The results are consistent with the benefit of embedding physics into the loss being therefore specific to the extrapolation regime and to the formulation tested, not a generic property of physics-informed learning. These findings are based on data from a single suburban site, and multi-site validation remains necessary before they can be generalized. By eliminating the need for continuous LiDAR operation after the training phase, the proposed methodology aims to enable cost-effective monitoring of multiple locations with a single instrument.