The fractal nature of the planetary boundary layer depth in the trade wind cumulus regime was explored. The boundary layer depths were derived from discontinuities in airborne lidar backscatter profiles obtained during the Frontal Air-Sea Interaction EXperiment(FASINEX) in February 1986. Scale-invariant behaviour was observed over horizontal distances ranging from 50 m to 50 km. The degree of intermittency and non-stationarity of the signals were calculated using standard multifractal statistical methods.