We propose a dedicated model to assist with the life cycle analysis of emissions of scientific computing centres. The model takes into account both the embodied carbon and emissions from use, as well as other factors such as data centre power usage efficiency, data centre expansion, hardware replacement, increase in energy efficiency of next-generation hardware, reduction in carbon intensity of the electricity supply and potential for heat reuse. If differs from existing models in its detailed handling of hardware embodied carbon and time dependency of various factors affecting the emissions. We present a number of scenarios where we apply the model to real-life HPC centres in different countries to illustrate how the trade-offs depend on the various factors and validate our model against the literature.