The CHE prototype is designed to estimate carbon dioxide (CO2) emissions using a modelling framework to link all the CO2 relevant observations with prior knowledge of the anthropogenic emissions and other natural fluxes that affect the observed atmospheric CO2 signal. The modelling aspects include atmospheric transport, atmospheric chemistry and land surface and ocean biogeochemical and transport processes, as well as statistical models of anthropogenic emissions of CO2 and co-emitted species based on human activity data. A multi-scale, multi-species and multi-stream approach is required to target the various types of CO2 emissions and natural fluxes, and their wide range of scales from point sources to cities, regions/ecosystems and countries. Different transport schemes suited for the different applications from local to global scales are listed and their challenges are described. The various approaches to estimate biogenic fluxes and anthropogenic emissions that serve as prior information are reviewed with their strengths and weaknesses. A comparison of the different transport models and prior datasets is proposed to assess the different capabilities of the models and priors used to perform the CHE library of simulations. Integration of the various components in the framework of Earth System Modelling is ongoing, with new developments on tracer transport modelling, simulations of plumes from emission hotspots, and urban modelling, among others. The full integration of the modelling and prior components towards a CO2 Monitoring and Verification Support (MVS) capacity will be presented in a final report on the design of the CHE prototype.