Abstract. Coral reef development is intricately linked to both climate and the concentration of atmospheric CO2, specifically through temperature and carbonate chemistry in the upper ocean. In turn, the calcification of corals modifies the concentration of dissolved inorganic carbon (DIC) and total alkalinity in the ocean, impacting air–sea gas exchange, atmospheric CO2 concentration, and ultimately the climate. This feedback between atmospheric conditions and coral biogeochemistry can only be accounted for with a coupled coral–carbon–climate model. Here we present the implementation of a coral reef calcification module into an Earth system model. Simulated coral reef production of the calcium carbonate mineral aragonite depends on photosynthetically active radiation, nutrient concentrations, salinity, temperature, and the aragonite saturation state. An ensemble of 210 parameter perturbation simulations was performed to identify carbonate production parameter values that optimize the simulated distribution of coral reefs and associated carbonate production. The tuned model simulates the presence of coral reefs and regional-to-global carbonate production values in good agreement with data-based estimates, despite some limitations due to the imperfect simulation of climatic and biogeochemical fields driving the simulation of coral reef development. When used in association with methods accounting for bathymetry changes resulting from different sea levels, the model enables assessment of past and future coral–climate coupling on seasonal to millennial timescales, highlighting how climatic trends and variability may affect reef development and the resulting climate–carbon feedback.