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Fluxes of trace gases, water and energy - the 'breathing of the biosphere' - are controlled by a large number of interacting physical, chemical, biological and ecological processes. In this interdisciplinary book, the authors provide the tools to understand and quantitatively analyse fluxes of energy, organic compounds such as terpenes, and trace gases including carbon dioxide, water vapour and methane. It first introduces the fundamental principles affecting the supply and demand for trace gas exchange at the leaf and soil scales: thermodynamics, diffusion, turbulence and physiology. It then builds on these principles to model the exchange of water, carbon dioxide, terpenes and stable isotopes at the ecosystem scale. Detailed mathematical derivations of commonly used relations in biosphere-atmosphere interactions are provided for reference in appendices. An accessible introduction for graduate students and a key resource for researchers in related fields, such as atmospheric science, hydrology, meteorology, climate science, biogeochemistry and ecosystem ecology.