His research integrates large-eddy simulation, satellite remote sensing, and high-resolution numerical modelling to investigate interactions among the atmosphere, climate, and human settlements. In collaboration with Richard Davy, he demonstrated that changes in atmospheric boundary-layer depth can substantially influence the effectiveness of climate forcing, a finding published in Nature Communications (2016) that has informed assessments of climate sensitivity in polar and continental environments. Satellite-based analyses of urban heat islands across 57 Arctic cities in Fennoscandia further revealed the reach of anthropogenic warming into high-latitude settlements, with important implications for permafrost, ecosystems, and infrastructure. His broader contributions include studies of Bjerknes compensation in the Bergen Climate Model, the role of the Barents Sea in Arctic climate dynamics, and the application of turbulence-resolving models—particularly PALM coupled with Enviro-HIRLAM—to air-quality management in cold-climate cities. Through coordination of the Nordic Council of Ministers’ TRAKT-2018 project and contributions to the Pan-Eurasian Experiment (PEEX) Modelling Platform, he has also promoted the integration of citizen observations, remote sensing, and high-performance computing into comprehensive environmental assessment systems. Professor Esau has established a distinctive research profile at the intersection of boundary-layer physics, Arctic climate science, and urban environmental modelling.