Atmospheric turbulence exerts a dominant control on the exchange of heat, CO2, water vapor, pollutants and momentum between the surface and the atmosphere, and therefore drives phenomena as diverse as climate, storm systems, air pollution, and glacial melt. Existing turbulence theory was developed for horizontally homogenous flat terrain, and fails in more complex terrain. Thus, for the majority of our planetary surface no viable theory of turbulence is available, and approaches that are known to be inadequate are nevertheless applied. The time is ripe to close this fundamental knowledge gap and formulate a theory universally applicable in complex terrain. Unicorn addresses this using a synergy of measurements, numerical modelling and theory to create a novel framework extending the existing theory of near-surface turbulence to complex terrain. Based on the ground-breaking hypothesis that including the directionality of turbulent exchange (anisotropy) can encode the boundary conditions, Unicorn will identify the key physical processes that cause anisotropy in complex terrain to differ from that over flat terrain. Thus Unicorn will systematically explore the parameter space of different sources of complexity, such as topography, flow conditions and heterogeneity, using unprecedented analysis of over sixty measurement datasets over flat and complex terrain coupled with machine learning approaches, sensitivity studies using state-of-the-art high resolution numerical simulations, and reduced order theoretical derivations. This synergistic approach incorporating the effects of complex terrain into a framework based on turbulence anisotropy will bring a much-needed breakthrough for understanding turbulence in complex terrain. Findings will revolutionize near-surface turbulence representation in numerical models, leading to better predictive capability in numerous societally and scientifically relevant topics, such as climate, extreme weather and air pollution.