One striking feature of coral reef ecosystems is the complex benthic architecture which supports diverse and abundant fauna, particularly of reef fish. Reef-building corals are in decline worldwide, with a corresponding loss of live coral cover resulting in a loss of architectural complexity. Understanding the dynamics of the reef architecture is therefore important to envision the ability of corals to maintain functional habitats in an era of climate change. Here, we develop a mechanistic model of reef topographic complexity for contemporary Caribbean reefs. The model describes the dynamics of corals and other benthic taxa under climate-driven disturbances (hurricanes and coral bleaching). Corals have a simplified shape with explicit diameter and height, allowing species-specific calculation of their colony surface and volume. Growth and the mechanical (hurricanes) and biological erosion (parrotfish) of carbonate skeletons are important in driving the pace of extension/reduction of the upper reef surface, the net outcome being quantified by a simple surface roughness index (reef rugosity). The model accurately simulated the decadal changes of coral cover observed in Cozumel (Mexico) between 1984 and 2008, and provided a realistic hindcast of coral colony-scale (1-10 m) changing rugosity over the same period. We then projected future changes of Caribbean reef rugosity in response to global warming. Under severe and frequent thermal stress, the model predicted a dramatic loss of rugosity over the next two or three decades. Critically, reefs with managed parrotfish populations were able to delay the general loss of architectural complexity, as the benefits of grazing in maintaining living coral outweighed the bioerosion of dead coral skeletons. Overall, this model provides the first explicit projections of reef rugosity in a warming climate, and highlights the need of combining local (protecting and restoring high grazing) to global (mitigation of greenhouse gas emissions) interventions for the persistence of functional reef habitats.This article is protected by copyright. All rights reserved.