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The accurate real-time detection of turbulent airflow patterns near airports is important for safety and comfort in commercial aviation. In this paper, a method is developed to identify Lagrangian coherent structures (LCS) from horizontal lidar scans at Hong Kong International Airport (HKIA) in China. LCS are distinguished frame-independent material structures that create localized attraction, repulsion, or high shear of nearby trajectories in the flow. As such, they are the fundamental structures behind airflow patterns such as updrafts, downdrafts, and wind shear. Based on a recently developed finite-domain--finite-time Lyapunov exponent (FDFTLE) algorithm from Tang et al. and on new Lagrangian diagnostics presented in this paper that are pertinent to the extracted FDFTLE ridges, the authors differentiate LCS extracted from lidar data. It is found that these LCS derived from horizontal lidar scans compare well to convergence and divergence suggested by vertical slice scans. At HKIA, horizontal scans are predominant: they cover much bigger azimuthal ranges as compared with only two azimuthal angles from the vertical scans. LCS extracted from horizontal scans are thus advantageous in providing organizing turbulence structures over the entire observational domain as compared with a single line along the vertical scan direction. In Part II of this study, the authors will analyze the evolution of LCS and their impacts on landing aircraft based on recorded flight data. [ABSTRACT FROM AUTHOR]