Significance A dataset from one of the last protected tropical peat swamps in Southeast Asia reveals how fluctuations in rainfall on yearly and shorter timescales affect the growth and subsidence of tropical peatlands over thousands of years. The pattern of rainfall and the permeability of the peat together determine a particular curvature of the peat surface that defines the amount of naturally sequestered carbon stored in the peatland over time. This principle can be used to calculate the long-term carbon dioxide emissions driven by changes in climate and tropical peatland drainage. The results suggest that greater seasonality projected by climate models could lead to carbon dioxide emissions, instead of sequestration, from otherwise undisturbed peat swamps.