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We develop a theoretical framework and analysis of the net land-to-atmosphere CO2 flux in order to discuss possible definitions of "emissions from land-use change". The terrestrial biosphere is affected by two perturbations: the perturbation of the global carbon-climate-nitrogen system (CCN) with elevated atmospheric CO2, climate change and nitrogen deposition; and the land-use change perturbation (LUC). Here, we progressively establish mathematical definitions of four generic components of the net land-to-atmosphere CO2 flux. The two first components are the fluxes that would be observed if only one perturbation occurred. The two other components are due to the coupling of the CCN and LUC perturbations, which shows the non-linear response of the terrestrial carbon cycle. Thanks to these four components, we introduce three possible definitions of "emissions from land-use change" that are indeed used in the scientific literature, often without clear distinctions, and we draw conclusions as for their absolute and relative behaviors. Thanks to the OSCAR v2 model, we provide quantitative estimates of the differences between the three definitions, and we find that comparing results from studies that do not use the same definition can lead to a bias of up to 20% between estimates of those emissions. After discussion of the limitations of the framework, we conclude on the three major points of this study that should help the community to reconcile modeling and observation of emissions from land-use change. The appendix mainly provides more detailed mathematical expressions of the four components of the net land-to-atmosphere CO2 flux

earth system dynamics

A theoretical framework for the net land-to-atmosphere CO&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; flux and its implications in the definition of &amp;quot;emissions from land-use change&amp;quot;