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Flooding is the most destructive natural hazard that humanity faces. Over a billion people globally are already exposed to the risk of flooding, but by 2050 this number is expected to double as a result of anthropogenic climate change, population growth, and encroachment into at-risk areas. Global Flood Models (GFMs) are vital tools for producing flood hazard maps supporting impact estimates, planning and policy interventions. GFMs typically assume that the bankfull flow-carrying capacity (channel conveyance) equates to a flow discharge with a specified return period (typically once in two years) that is spatially and temporally invariant. However, in reality, conveyance capacity is determined by the river channel size, shape and roughness and so varies in response to erosion and sedimentation - change that is presently unrepresented, which biases GFM predictions to unknown magnitudes. Herein we address and evaluate these questions by applying the Fathom GFM to estimate inundated areas and population exposure across a 135,000 km2 region of the Mississippi River floodplain by forcing the model with an empirically-constrained range of space-time varying conveyance capacities. We find that these estimated conveyance capacities (typical RPs < 1yr) differ substantially from the 2-year RP often assumed, leading to substantial underestimates of flood hazard predictions (up to 20%) and consequent underestimates of population exposure (up to 52%). These results indicate how geomorphological variability is a first order control in estimating flood hazard and risk, and that it is therefore vital such changes are included in flood hazard and risk formulations and predictions into the future.