Turbulence in the atmospheric boundary layer (lowest layer of the Earth’s atmosphere) plays an essential role in weather and climate, as it is the key process through which the heat, moisture, mass (e.g. various gases, pollutants), and momentum are transported between the Earth’s surface and the atmosphere. Accurately representing the effects of this turbulent exchange in numerical models is therefore crucial for accurate weather predictions and climate projections. Directly modeling turbulence in numerical models is, however, impossible for any practical purpose due to turbulence’s chaotic nature across different scales. Currently, virtually all numerical models of atmospheric and oceanic flows therefore parametrize this exchange though a statistical approach called Monin-Obukhov similarity theory (MOST). Developed in the mid-20th century, MOST is based on assumptions of flat and uniform terrain under specific atmospheric conditions which are not met over the majority of the Earth’s land surface. Over mountains or polar regions, MOST routinely fails. This failure is manifested through large scatter in MOST predictions, as turbulence is deformed by terrain-induced processes and atmospheric stratification in as yet not fully understood way. This mismatch and the use of MOST beyond its limits of applicability adds uncertainty to weather prediction and climate projections. The overarching goal of Unicorn is to increase our understanding of complex terrain turbulence, and modernize its modeling by taking into account the influence of topography and atmospheric stratification. With this knowledge Unicorn aims to develop a novel turbulence theory valid over terrain types ranging from flat and uniform to highly complex, and over a wide range of atmospheric stratification. This will ultimately lead to parametrizations able to correctly represent the effects of complex-terrain turbulence in models of atmospheric and oceanic flows. The new theory and derived parametrizations will improve the accuracy of weather forecasts and climate projections in regions most susceptible to climate change, such as the polar zones and mountainous areas, thereby supporting more effective climate adaptation and mitigation strategies, as well as help in resource management, preparing for extreme weather events, and making informed decisions affecting environmental and public safety.